PROS:

+ Strong early clear.
+ Unique paths to gank due to his E Shadow Step
+ A lot of mobility.
+ Adaptability/ Fits in every team.
+ High burst as Assassin.
+ Very tanky as Rhaast.

CONS:

- Weak without form.
- Steep learning curve.
- Vulnerable to crowd control.
- Not reliable crowd control for ganks.
- If stomped early hard to recover.

Flash
For sure can't be replaced by anything. Used both offensively and defensivly on Kayn and it's utility is great. You can close or increase distance between you and enemies, get over walls, dodge skillshots etc. Although it's long cooldown is your best choise.

Smite
Irreplaceable! Not taking smite when jungling is trolling. You lose, clear speed, health and risk losing objectives like Dragons, and Baron nashor.

Chilling Smite
Can be used on Rhaast and Shadown Assassin too. Usually when enemies have a lot of escape potential like high mobility but also when you need mobility for escaping a fight. Also you can smite an enemy and use R Umbral Trespass to hop in and avoid damage or chase down.

Challenging Smite
Can be used on Rhaast but it is not advisable on Shadow Assassin because with him you want to avoid extended fights. Your spike is to go in, combo and out. If you don't achieve your goal, get out wait for CD and go in again from different angle. Don't be predictable, don't overstay in a team fight you will die. On Rhaast can be used if the enemy jungler has also challenging smite and you are about to duel him early for any reason. Usually with bot Kayn forms you want to avoid dueling and/or skirmises early beacuse you are very vulnerable.

Shadow Assassin

I am not very keen of Electrocute cause it is mainly for early-mid game where Kayn focuses mainly on farmiing and easy picks. Dark Harvest on the other hand has insane late game scaling where you really pop of and start doing tons of damage. Some may say that Electrocute can be used to make up for bad early game so you have like bad early game but good early rune and then bad late rune but good late game. Personally i thing this isn't optimal and that you should choose Dark Harvest for extreme mid-late game. Just play it safe early, farm, look for picks, secure drakes if that is possible and of course dont /ff. Sudden Impact for extra lethality in every Reaping Slash. Eyeball Collection for extra burst and Relentless Hunter to get more mobility. Secondary i chose Magical Footwear for the extra bit of mobility (since they have +10 movement speed) and also to save yourself 300 gold which synergises with Future's Market to help you get to your powerspikes easier in case you get behind or even faster if you are doing ok.

Darkin Rhaast

For Rhaast runes are pretty standard, Conqueror is your best bet even though they nerfed the healing it is still the best option since you heal a lot from your abilities and of course Goredrinker. Rest of primary are pretty self-explanatory Triumph for sustain and surviving these close fights, Legend: Tenacity to be harder for the enemies to lock you down and Last Stand because you will be going low on Hp a lot and then heal back up. Secondary Sudden Impact for lethality in every Reaping Slash and more healing from Ravenous Hunter.

Shadow Step [E]

The greatest ability in Kayn's arsenal is Shadow Step. This ability allows him to travel through terrain at high speed which makes him an insanely powerful ganker. Without solid vision, the enemies don't know where he'll hop out and begin slicing.
Shadow Step forces you out of terrain at the nearest edge indicated by a dark dot/circle. Be sure to position yourself at the optimal position to gain maximum distance travelled when the ability ends.
The small heal from Shadow Step can be the difference between life and death. Hop into terrain when getting low in a fight.
It's even useful in mid-lane to approach your target quickly. Use Shadow Step to run through the walls travelling parallel with the river.
Remember, you can also travel through the map's outer walls, you can run along its edge to get into lane faster, and also to chase enemies who are trying to escape.

Umbral Trespass [R]

Once you've hopped into someone, you go where they go. If you see an enemy trying to escape, hop inside and they can't avoid you.
Umbral Trespass is a great way to avoid CC, like Leona's ultimate Solar Flare
Think carefully about your exit. You want to block paths to escape as much as possible.
Remember that the longer you stay inside an enemy, the more time their cooldowns have to refresh as well as yours. If they're low on health, you may be better off exiting sooner rather than later.
Umbral Trespass will reset tower aggro, giving Kayn the potential for insane tower dives.
When playing as Rhaast, you'll want to time your Umbral Trespass to grant the biggest heal possible, so consider waiting to tank some damage before you jump into your enemy so when you exit they have nothing left to burst you since you will be above half HP for sure. Even fully healed.

Try to powerfarm for the most of the early game to get to mid-late game and start one-shotting people. Constantly move your camera at lanes and look for free kills. After getting Manamune spam E Shadow Step and Q Reaping Slash to move around the map faster. Usually by constantly using your Reaping Slash to move you play the game at around x1.25 speed so be sure to get that extra mobility!

In late game you fall of a bit, Though you still can one shot carries and turn around team fights. Take care as the enemy will build a lot of items to counter you (like Zhonya's Hourglass and leave you in a team fight standing and watching the ADC who you would R Umbral Trespass turn gold and your screen turn grey. Try to flank in team fights from unexpected angles and wreck the enemy backline.

Again powerfarm is your best bet for mid-late game scaling. Make sure to don't miss the chance for free kills at lanes. Rush Ironspike Whip to help you farm and fight. After getting Goredrinker you start to heal a lot and be tankier so watch out for grievous wounds that the enemies might use to counter you.

You are an absolute healing monster. !! Watch out for grievous!! they will get you by surpise when you don't notice them and may lead to death. Look for frontlining and peeling. When low, trigger Goredrinker and try to hit as many enemies as possible. Or R Umbral Trespass someone with lots of Hp to get out or R with full Hp. You are a big trouble and the enemies will try to burst you down quickly to get rid of you so be careful.

When the enemy jungler reveals himself, and there is no objective on the map to get or any play to happen, you can counter-jungle the opposite quadrant. Or when they die you can sneak steal his buffs and make him really frustrated. Also, you can leave one small Murk wolf or one small Raptor or from the 2 original Krugs the small one to prevent the camp from respawning. This way you mess up his camp sequence and leave him behind as far as gold and exp are concerned. When the enemy jungler goes to that camp he will have to kill the small monster for little exp and gold and wait until the camp respawns again to take full advantage. If you can do this in his red buff quadrant, he will have 2 camps stalled and his buff missing, and he will be quite upset. If there is an objective, you can abuse the fact that the enemy team’s smite is far away and go for it without risk or make a play like a potential tower dive on the opposite side of the map.

Always check for enemies who shove waves into your tower when your laners are missing (dead or recalling). These minions are wasted and why not take advantage of some free gold and exp.

Do not force ganks except if you really need to (for example, placing a rift and getting the gold from the plates). You mainly want to powerfarm but do not think ganks of a way to mess up your clear and disdain them. You maybe get a kill or if not, you will get exp for sure and some gold that you will tax from the lane minions. Usually if you do not get the kill get some minions but if you do get the kill it would be better to not touch any of them (unless your laner asks to) to prevent them from tilting.

If you get ahead of the enemy jungler you can start counter-jungling even without them revealing themselves. You will have level advantage and thus stronger smite to steal away camps. Or you can just 1v1 them in their own jungle and make them go AFK after. But be very careful about lane priority since getting collapsed and shut down can be detrimental. So do not get cocky.

A very helpful way to look at lanes is to unbind the option “Select Ally 1”, “Select Ally 2” etc. from the F-keys (F1, F2, F3, F4) and bind them in easier to press keys to be able take glances at your laners and gather info about the lane state, if it is gankable, etc.

When counter jungling try to place some form of vision deep into the jungle to be able to keep track of the enemy jungler, while protecting your team and giving you the opportunity to spot him and make some sort of play around the map either is an objective, a dive or even a simple gank.

About the orbs,
when attacking ranged champions you get blue orbs that will tranform you into Shadown Assassin. When attacking meleee champions you get red orbs that will transform you into Darkin Rhaast. But what about Nidalee or Jayce or Elise etc? When attacking them and they are melee form you get red and when they are in ranged you get blue.

Generally Kayn is countered by champions with high burst (one-shot) potential and lots of CC. If he gets locked down he has no escape tools but the point is to never let the enemy lock you down with constantly spamming Shadow Step and Reaping Slash.