Kayn is actually very good and fun to play, let me give you a few tips.
Base kayn sucks, so you NEED to get a form. So I won't give any tips on the base form just keep hitting champs to get orbs.
He has a couple key items I recommend for him in either form,
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Rhaast:
1 - Build him a tank with warmogs and sterraks, and to make him a tank with tanks for wheels, give him a death's dance, BORK, and black cleaver.
2 - his q you should max first, it can do a lot of damage even towards tanks.
3 - his w should be maxed second, it does a fairly decent amount of damage with a serious knockup.
4 - his e should be maxed last, it's still fairly decent of an ability, but you want to have as much bruising as possible.
5 - his ult isn't mean to be a "massive damage nuke" it's supposed to be a way to regain health (mostly if you do it on tanks) and to wait for cooldowns a little longer.
6 - he can be a massive god in a team fight because of his knockup, and if you build him a tank and engage with also your ultimate, you give no cheese about the enemy team.
7 - if you also have the build I mentioned on #1, give him gargoyles to make him even more hard to deal with in a team fight.
8 - this guy can hard counter some champions that are very powerful in team fights, such as yasuo, tryndamere, and so on. HE EATS THEM ALL FOR BEKFAST
Shadow Assassin:
1 - always build duskblade and youmuu's, lethality is a large part on this form.
2 - you may also want to build boots of mobility to do a swift engage.
3 - to make tanks cry, give him BORK and black cleaver.
4 - max your w first since it's way more useful in the damage compartment in this form than the q.
5 - max your q second the damage is still good.
6 - max your e last yet again.
7 - your ult you should use after 3 seconds, which is the duration of your passive in this form. Because it resets your passive plus it does a lot of damage.
8 - when you are shadow assassin, you are most effective with doing quick kills to targets that are alone.