This is the build that I have been using to this season (season 8) to get 100% win rate with Kayn. I find it gives a nice balance of Damage and sustain, and provides amazing tanking ability!

It is crucial that you take Dark Harvest from the Domination tree as you are playing as more of a tanky bruiser, taking Rhaast,
rather than shadow assassin. W,Q,AA (W,AA,Q if close enough) combo becomes super strong with dark harvest and deadman's plate.

1) Stalker blade for CD, damage and slow.
2) Black cleaver for health, CD and Damage
3) Titanic hydra as opposed to ravenous hydra for the health, as we are going for a more of a bruiser/tank build + AA reset
4) Spirit visage mainly for the passive (30% increased healing) which just makes you a monster together with Rhaast's passive, but also for the MR.
5) Deadman's plate good tank item + passive buffs your AA and works well with Dark Harvest
6) In case there is a Fiora, Zed, Kha'Zix, Jinx team comp you can get Thornmail to show them the salt :D
7) Guardian Angel if late game smiting people doesn't make a difference.

The amount of damage you can put out is absolutely ridiculous, taking into account the fact that you are mostly playing as a tank. The sustain from Rhaast's passive, together with spirit visage, makes you almost impossible to not heal from 0 to full in one sweep of your Q. Deadman's plate and spirit visage provide the resistance, while Titanic Hydra and Black Cleaver add extra health and damage. Over all this is a very well rounded build which I find suits all situations with little adjustments here and there!

Enjoy and good luck on the fields of Justice! :D