Hello,
My name is Archimagirus and I've been playing League of Legends since early Season 3, maining jungle the entire time.
This is my first attempt at making a guide, so please, be gentle. Comment with any questions or concerns and I'll do my best to improve the guide however all of you see fit.
Kindred is the first champion I've gotten genuinely excited about in a long time, because her being released is a sign that we're FINALLY moving away from the tank meta that I've gotten so bored of over the last two years, and it opens up a lot of really interesting possibilities for team composition.

Pros

- Very Mobile
- Huge Damage
- Incredibly Snowbally
- Infinitely Scaling % Health Damage
- Decent Sustain
- Game-Changing Ultimate
- Kiting Makes Jungle Clearing More Interesting

Cons

- Squishy
- Easily Counter-Jungled at Level 1-2
- Badly Timed Ultimate Can Ruin A Teamfight
- No Hard CC
- Hard To Play From Behind

Mark of the Kindred

Kindred's Passive is one of the biggest parts of what makes Kindred such a powerful champion.
Mark of the Kindred allows Kindred to gain stacks for killing marked enemies that add a % current health damage to every one of Kindred's auto attacks. This inspired Kindred to counter-jungle when wolf marks enemy camps, and to gank often to get as many stacks as possible. This also gives Kindred incredible mind games to play at higher ELO, as when someone gets marked they will announce it, and other lanes will assume you're not headed toward them.

Dance of Arrows

Kindred's kiting skill, and main source of damage early game.
Dance of Arrows allows you to close gaps, dodge skillshots, and jump over small walls all while having respectable early game AoE damage. It's cooldown is reduced to 2 seconds while inside the area from Wolf's Frenzy, which allows you to easily kite jungle camps to keep your health up and to generate stacks for Wolf's Frenzy's passive.

Wolf's Frenzy

Wolf's frenzy is taken first, but maxed last.
The passive heal allows you to sustain in the jungle, and along with the extra damage it provides, the active brings your Q's cooldown to 2 seconds while inside the area.
It is worth noting that if you cast Dance of Arrows before Wolf's Frenzy, it will still reduce the cooldown to 2 seconds from whatever it was at previously. This means that when engaging a fight over a wall (for instance jumping in to contest dragon from bottom side) you should hold on to Wolf's Frenzy until after you jump over the wall so that wolf will be able to do his damage, and you will have more space in the area to move around.

Mounting Dread

Kindred's only cc, and a percent max health nuke.
Mounting dread while flanking an enemy is the best way to start a gank, especially early game before your damage gets amazing. It is also great to use while running away right before hopping over a wall, because even if they flash after you they will be slowed and you'll likely escape. It is also worth using in the tankier jungle monsters early game to make your clear easier, but only if you have blue, because without blue you can't afford to use it so regularly.

Lamb's Respite

Lamb's respite is your unique game-changing ultimate.
Inside it nobody can die, including your enemies. When it ends everyone inside, including your enemies, gets healed. This can set up some unique opportunities for your team, allowing an adc to tank a nexus turret for 4 seconds without dying, or assuring nobody on your team dies while diving past a turret. This skill is excessively strong when you have a team with strong area control and displacement. If you have Azir, Tristana, or anybody else with displacement skills your enemy can be knocked out of the area before the heal goes off and finished off, winning you the fight. But keep in mind the same can happen to you. Do not use this to kill your entire team.

Greater Mark of Armor Penetration
With Kindred's low AD scaling, this guide is for an on-hit focused build. Most of your damage will be coming from your passive and Blade of the Ruined King, so armor penetration will increase your late game damage by a lot more than a few flat attack damage would.

Greater Seal of Armor
These are pretty standard seals for everyone, and they help you survive jungle clearing at early levels. There's nothing else that would fit here better.

Greater Glyph of Scaling Magic Resist
You won't really feel these early game, but late game they could be the difference between you surviving long enough to pop your ult on your whole team and you getting erased by a fed APC in one combo and doing absolutely nothing. They're must-haves.

Greater Quintessence of Attack Speed
Again this is an attack speed & on-hit build, so flat AD wouldn't add much, but attack speed helps a lot.


Other Viable Options
Greater Mark of Attack Speed
If your team uses you as an excuse to use an interesting composition with someone like Mordekaiser or a second AP carry in the bottom lane, the opposing team likely won't stack too much armor and attack speed could be a viable option.

Greater Mark of Attack Damage
Greater Quintessence of Attack Damage
I would recommend these for my warrior build. Take them if your team has a weak early game, and you intend to take the warrior enhancement just to survive help your team survive early. It won't be ideal, but you gotta do what you gotta do.

Without going in to too much detail, the offensive tree is a pretty standard AD carry set up, but without Warlord and Frenzy because I don't recommend building very much flat attack damage, or any crit chance.
I use the utility tree instead of the defensive tree because with Kindred's kiting ability, I believe Fleet of Foot, Summoner's Insight , and Runic Affinity help a LOT more than a little bit of extra health.

Stalker's Blade vs Ranger's Trailblazer

Ranger's Trailblazer allows you to clear camps at higher health, and to stay outside of your base longer. Stalker's Blade gives you another much needed slow. I recommend Stalker's Blade once you're comfortable, but Ranger's Trailblazer until then. Also, in bad matchups I recommend Ranger's Trailblazer just so you don't get completely destroyed by their counter-jungling.

Enchantment: Devourer vs Enchantment: Warrior

Devourer was nerfed recently for ranged champions, but with Kindred's passive late game the attack speed is still significantly better than the extra damage and armor penetration on Warrior. It also adds magic damage to every attack so you're harder to itemize against if you're the only one snowballing. Warrior however, is significantly stronger early game, so if your team is really struggling it is worth taking. I only take warrior if I won't have time to farm up my stacks in the jungle.

Berserker's Greaves vs Mobility Boots

The added attack speed from berserker greaves is obviously fantastic for the Devourer build, with it's 3 separate damaging on-hit effects. Boots of mobility though are also very helpful if you need to have huge map pressure, or if you're having trouble getting vision. I can't condone counter-jungling without vision, but counter-jungling is always safer if you move faster.

Blade of the Ruined King

Blade of the Ruined King is awesome for the Devourer build on Kindred. It increases attack speed to get even more procs of Mark of the Kindred and Devourer, while adding another percent health on-hit effect of it's own. This is like having a second Kindred passive at 8 stacks as soon as you buy it.

Runaan's Hurricane

Runaan's Hurricane applies on-hit effects, and has the highest attack speed boost of any item in the game. What could be better than hitting percent health damage more often and on more people? Runaan's Hurricane is a huge power-spike for your team-fighting. No front-line can survive you with it.

Zephyr

Move speed, attack speed, and tenacity. All the kiting potential.

Last Whisper

Great armor penetration item, which helps with the BotRK and Mark of the Kindred damage.

Frozen Mallet

On hit 30% slow, and a little health. This is a great last item for the Devourer build, as it makes your kiting even better.

Youmuu's Ghostblade

The active on this really adds some turret pressure for Kindred, and makes the Devourer build a little burstier with the active. The moves peed buff also helps with escapes.

Wit's End

Attack speed item, adds some magic damage on hit. Great item if your team lacks a strong AP champion, or if your enemies buy more than one Thornmail to deal with you.

Black Cleaver

Stacking armor shred, plus move speed on hit. This helps with your chasing and kiting, but is probably only worth getting on Devourer Kindred if your ADC is doing well. Helping someone strong do even better can be devastating, but if your ADC is feeding, or just hasn't been able to farm effectively this won't save them.

Trinity Force

This gives everything anyone could want. The spellblade passive is what makes the warrior Kindred build work, and gives you some pretty decent poke and amazing burst.

Bloodthirster

Huge flat attack damage helps with spellblade passive damage on warrior build Kindred. It also gives you a small shield to keep you alive a little longer.

Sterak's Gage

Sterak's gage is pretty awesome with Kindred's ult. You get bursted, but can't die, and then get huge with the passive and do even more damage. I would only get this on the Warrior build.

Maw of Malmortius

Good for Warrior build Kindred if you're scared of AP burst.

Mercurial Scimitar

Great for Warrior build Kindred if you're getting chain stunned a lot.

Kindred's first clear can be a little bit rough. Start on the camp closest to bottom lane, and move on to your first buff. Don't forget to keep kiting, or you will die. Once the scuttler crabs spawn one of them will likely get marked by wolf. Take the one closer to bot just for the life-steal from your W, and if it's the marked one congrats, you just got your first stack.
Remember while jungling with Kindred, smiting Gromp won't do much for you because you want to be kiting. Smiting golems is good because the stun gives you a lot of time where you aren't getting hit, and smiting Raptors is good because it lets you clear wards while you counter-jungle, so they have less of an idea where you are.
Go back if you're low, and head over to your second buff. After second buff, start looking for ganks.
Mark any lane that is pushing past river with your passive, and wait a second and watch what happens. If they pull back, start looking for another jungle camp marked by wolf. Don't forget to ward while counter-jungling, and not go if they have a strong duellist jungler who you don't have vision of. If another lane starts pushing harder, go gank there. If neither happen, go gank the guy you marked and hope you get another stack.
Always remember to ping your intentions. If you mark the half-health support and your team focuses the full health ADC, you might lose an easy stack. Also, Kindred doesn't have the CC to solo kill people on ganks unless they're really low, so your lanes will need to engage while you come in.

Mid game you should be focusing on getting stacks for your Devourer.
Also keep an eye on dragon, with all your percentage based damage Kindred has amazing dragon killing potential. You can solo it pretty easily at level 6, and if you keep vision up you should be able to tell if it's warded. I like to mark a lane that's pushing so they'll back off, then just go solo dragon as soon as I have BotRK while they wait for me to gank.
You should also be helping with turret pushes. With my Devourer build you don't do much damage to structures, but your Ult alone can be enough to pick up a kill or to scare them off their turret so your team can take it.
Try to get your team to communicate well, and always remember to ping your intentions. If they don't know what you're planning, and the enemy team comes, you might waste your ult while your team runs away, or even die. Kindred can kite well, but there's only so much kiting you can do.
When going for objectives, always remember to mark the person you deem most likely to die fighting over that objective on the enemy team. If there is a 0/11 Soraka on their team mark her, and kill her first. It doesn't matter if she isn't worth any more gold or experience, a stack is a stack, and a stack is great.

By late game you should have Devourer, BotRK, Runaan's Hurricane, and boots. Your devourer will be sated, and there is no reason for you to be clearing jungle camps any more. You should be with your team forcing objectives. Or, you can send your team out to distract the enemy team while you take objectives. Kindred can solo dragon early, and if you do well stacking your passive she can easily solo Baron if you make sure the enemy team isn't paying attention.
Don't forget to upgrade your trinket, buy pink wards, and always be safe. A dead Kindred is a useless Kindred.
Your job in team fights is about the same as any other ADC. Position well, so your front line can protect you, and melt the enemy team. You are even better at killing tanks than most ADCs, although your %based damage will be less impressive fighting other carries than the huge crits a normal ADC would have. You don't have to focus carries, just kill whoever is closest to you, and don't get caught.

In conclusion, I believe Kindred is an incredible addition to the League of Legends Lineup, and will open up a lot of possibilities for team compositions.
She's a strong, fun, and interesting jungler.
I believe my builds are the best way to play her, and I hope you guys agree.
Before down-voting, please try the builds a couple times and let me know what you like and dislike about it.
I'd love some feedback.

Cheers,
Archimagirus