The Kayn Problem
In Kayn's current state, Darkin form is really the only one you should be picking. He deals good damage, has incredible sustain, and his cc is a great tool at such a low cooldown. Shadow assassin leaves a lot to be desired, it's fast and hurts, sure, but lacks any escape or surviveability so he might get a kill but he'll quickly get shut down by a competent team. IMO Darkin is in a pretty good state, but shadow assassin needs buffs.
Through several games of playing I've noticed shadow assassin's ult is lackluster. It resets his damage but the second he comes out unless it kills he'll get shat on. Killing is hard however when the ability doesn't really deal much damage and they have time to prepare for it. The shadow assassin ult seems to need damage buff and possibly a heal to keep the poor guy alive, healing only on his e really isn't enough for him, given how squishy that form is.
The e in shadow assassin form also feels irrelevant, he Sonics across the map but it doesn't do anything in combat, possibly make it reset on kills or at least be able to be used viably in combat for a quick escape/heal. Just a few suggestions, but something definitely needs to be done about the Shadow Assassin.