The key to playing Kayn is to be like headphones kid from Synapse. So basically you troll people and take enemy jungle camps and when the laners come dip with your E. Since most of your time is spent in the enemy jungle, take that opportunity to gank wherever you want from behind. Remember to never gank bot lane unless they have a melee support, because you want Rh'aast by 5 minutes. If enemy bot lane has a Yasuo ADC, run it down mid lane 3-4 times to try to increase the other team's odds of winning and make the game more fun for you.

After you have red form, you have won the game. Rush every deaths dance after warrior for extra spiciness. After an item or 2 and red form, you just have to continually press Q and W, and remember to ult the tankiest dude early in the fight, to take advantage of pesky enemy ability cool downs.