I know Kayn hasn't been out for super long but I have found something that makes Shadow Assassin just as effective as Rhaast/Darkin Form!. This is my short guide on how to stab butts from the shadows.
Basically Kayn has a pretty bad early game as some of you Kayn players can tell. It's not that good, which sucks cause I wish he was as good as some champs like Lee, but he isn't so we just have to deal with it. Shadow Assassin makes you really good mid-game, but not too good late (Unless super super fed.) so be aware of that fact. Kayn's Shadow Assassin form is what makes him so good mid game, his passive is a Scaling Percent of your recent Damage dealt over three seconds that comes back as magic damage. (DON'T PLAY AP KAYN I TRIED LMAO.) This passive alone makes you really dangerous, but if you also take TLD into account, you're bursting pretty flippin' hard. Since you also build Lethality Second (Now really good if you're ahead since it scales with your level rather than the enemies level) this can make you a monster mid game for any squishier champs(ADCs or Squishy Junglers/MidLaners.)The way you wanna play Shadow Assassin Kayn is save your flash for escapes, jump onto your first Target, Q-W combo followed by the Auto to pop TLD, Smite them, and if they're low enough to kill with an Auto, just do it. If they're not and some people are closing in on you all you have to do is Ult them, Slide out to the nearest target that is squishy or low health, and do your full combo again since your ult refreshes your passive. If they die off of this and you get the double, just leave and don't be greedy. Put your E to use and book, but if you're really fed and think you can do it go for more picks since you just took down two people! That's all I really have to say, I will be sure to update this guide the more I play Kayn seeing as he's only been out a short amount of time and I still have alot to learn!