Kayn is a really balanced champion, his early game is kind of weak but if you let him into mid-late game, he becomes a monster. Rhaast allows the player to have massive sustain during big team fights along with the ability to shred tanks while being a tank. Shadow Assassins on the other hand can assassinate enemies under 1 second with the ability to fly through walls, ambushing the enemy. With that being said, this is a guide on how to play Kayn.

Also give me some suggestions if you actually read everything :D
I will try to post some gameplay as well.

PROS(Rhaast): Fast Clear
Late Game Monster
More Escape Routes
More Creative Ganking Routes
Ult heals you a lot.
SHRED TANKS.
SUSTAIN.

CONS(Rhaast): Weak in Kayn Form
No Damage Early Game
You'll get anal'd if you don't land your W on adcs.
Can easily get kited.

PROS(SA):Fast Clear
Mid-Game Monster
More Escape Routes
More Creative Ganking Routes
Can easily one shot squishies
Easily chase down enemies with shadow step.

CONS(SA):Weak in Kayn Form
No Early Game Damage
No Sustain in Jungle
Really bad late game, kind of like kha zix.
If enemy has cc, you're screwed.

Blue Side:
Red Buff ---> Raptors ---> Wolves ---> Blue Buff ---> Gromp

Red Side:
Blue Buff ---> Wolves ---> Raptors ---> Red Buff ---> Golems

Rhaast: As Rhaast, your job is to kill the enemy carry's peel, which means you kill the tanks, because Rhaast does a **** ton of damage to enemies with a lot of health, and if you ult on the tanks, you will probably gain back 50% or more of your health, to be safe, use it when you are at about 20% health. However if the carries are vulnerable, trying knocking them up with your W to prevent them from escaping, and if you are fixed on killing the carry, everyone will aim for you so make sure you have time to hit and ult a tank to heal back up.

SA: Shadow Assassin's team fight is really bad like Kha Zix's, he cannot go in directly or else he'll get blown up. In team fights, try to use the terrain to your advantage, since Shadow Step grants extra movement speed, flank around to their back line and assassinate the carries, and if you are getting focused, simply ult their carry, making their team distracted and let your team do all the damage.

As Kayn, your Shadow Steps gives you the ability to move through walls, allowing you to gank in creative ways. If the enemies are pushed up and your laner does not have cc, shadow step through the enemy's jungle and surprise the enemy, however if your laner does have cc, shadow step through your jungle and chain cc the enemy.

Since Kayn does not have any gap closers, try shadow stepping right next to the enemy and attack them with your Q and auto attacks, save your W for when the enemy is out of auto range, then use your W and catch up.

The first thing that comes to the enemy's mind when you ult them, is to either walk under tower or walk to their team mates, and that can really screw you over.
As Rhaast, you either ult the tank for health or you could ult a squishy to secure the kill(if their health is low enough), it does not matter when you're ulting tanks because they don't need protection and they're fat enough to withstand Kayn's ult damage(low as hell), however if you're ulting a carry to secure the kill, try to get out as soon as possible to prevent the squishy from healing up, then focus on killing the tanks from their backline, and since you're also fat, you don't have to worry about getting bursted down upon leaving the carry's body. Shadow Assassin needs a lot more decision making, since he is just an assassin, so he'll get blown up straight away in a team fight. When you ult, always make sure you are ulting a damage carry, either for kill secure or gap closing, either way, you have no reason to ult a tank. When you ult a squishy for gap closing, their whole team will be ready to burst you down right as you come out, in this situation, try to ult back out after your Q and W are off cool-down, and away from the carry's team mates then go back in and finish them off the instant you get out of their body. If you're lucky, you will be able to get out if your team back stabs enemy while they try to burst you down, but if your team does not know what to do, you're basically dead.

Rhaast(Can't really one shot because of the bruiser form, so this for long fights):
E(for getting close to enemies) + W + Q + AA + AA + AA + AA + Q + R(wait for abilities to go off cooldown) + W + Q + AA

SA(For Squishies, SA can't really do anything against tanks):
E(for getting close to enemies) + W + AA + Q(if not one shot, + R(wait for abilities to go off cooldown) + W + AA + Q)

It always depends on the enemy team comp, if they have 1 or no tank, then try to go for Shadow Assassin, mainly because he deals massive damage with my build, and since the new Duskblade is broken and his W and Q are enough to easily take away 70% of the squishy opponent's health, and add an energized(Statik Shiv and IE crit) auto, they're basically dead, and you can do that like every 10 seconds, since your ultimate is not needed to assassinate someone. But if you want to play safe and don't think you can end the game early enough, go for Rhaast. If the enemy has 2 or more tanks, its probably the best to go Rhaast, because of all the tank shredding and sustain you have, plus League is broken so tanks = wins, and Rhaast is a tank and a tank shredder, so double win for you.

Overall Rhaast is the safer option for you, no matter what team comp they have, because the other team's dps may out damage your if you go Shadow Assassin, so choose wisely.

-It is still possible to die during your ult, so try not to ult last second
-Zed's ult will still pop if you're in ult, so try ulting Zed right as he comes out of his ult(his ult deals damage based on the damage he dealt when his ult is still active) to avoid damage
-Outplay your opponents with ult(Riven, J4, Wu, Yasuo, etc)
-If the enemy is a counter-jungler(like Lee or Shaco), never use your E to heal for clearing jungle camps, always save it for escaping(may be different for low-elo)
-It is possible to steal baron and dragon while Shadow Stepping through the walls