If you're looking for an interesting Kai'Sa build - I have one for you
Kai'Suh dudes
I might regret shining light on this build, it's been my little OP secret. But if you're looking to explore Kai'Sa, I've been taking her mid with a rather unique build based around assassinating.
Runes Domination: Electrocute - Sudden Impact - Eyeball Collection - Ravenous Hunter Sorcery: Ultimate Hat - Transcendence
This optimizes both her burst and her survivability. The extremely low CD on your ult with this build will keep you dashing around for sudden impact burst, while Ravenous offers immense healing with your Q mechanics, which I will explain more in-depth later in this post.
Item build
Starting:

The reason I start dark seal is because with only 2 stacks, it will save you 435 gold later in the game.
Core Items:
Once you finish this item, you can immediately start one shotting people. The 15% healing scales sooo well with her Q, because it counts as a single target spell even if it hits different things. So it gets full 30% (Gunblade and 5/5 Rav. Hunter) healing from the damage it deals, which when upgraded, can be huge numbers.
This slot doesn't really make a huge difference in what you buy, as long as the items offers AT LEAST 55 AD. Although, it might be expensive, if you can afford it
healing stacks multiplicatively with Gunblade AND Rav. Hunter. (Meaning 45% healing on her Q) Duskblade is cheap, and cheap tho. :)
If by the time you finish your gunblade and don't have 2 stacks on dark seal, drop 435 on this just to upgrade W. It makes a difference, and you will be building it into stuff later.
Final Build Example

I take mainly AP because her burst scales crazy with high AP. I've gotten my Q to do upwards of 1700 damage to a single target with full AP, all the while healing for 30-45% of that. Still get a massive shield from ult, and W will easily take squishies to >50% HP.
How to play the build
Level 1: Take W, and immediately start trading with your lane opponent. (Unless you're being absurdly outranged) You should be positioning near their ranged minions until level 3/4.
Early game: Try not to shove, although it is hard with the way Kai'Sa has to trade with her lane opponent. If you are shoved, don't be afraid to roam. You don't need to be 6 to get efficient ganks.
Mid game: With your gunblade finished, you should be looking to snowball the game. Constantly roam, fish for W hits. You should be strong enough to win any 1v1 with gunblade.
Late game: You should be positioning safely behind enemy lines. Stalk at your max ult distance, once a fight starts, try to land a W on a squishy, then go in with your R. If you fail the W, you can always ult to someone your team has CC'd too.
Combos Level 1 combo: Auto x3 -> W to pop passive/electrocute. Extreme squishies like Karthus might die outright to this with an ignite thrown in. Level 3 combo: E to close distance -> auto -> Q -> Auto x2 -> W to pop passive. Gunblade combo: Auto ->W -> Gunblade+Q -> auto. This should pop your passive, and do horrific amounts of damage. Long range assassination: W -> R -> Q+Gunblade -> auto. You might need an extra auto, but if you're ahead this will normally outright kill someone. Re-position combo: Auto -> w -> r -> q+auto
As for your E, because you're not evolving it I normally use it to create/eliminate distance since it's pointless to use mid fight specifically for DPS increase.
Conclusion Thank you for reading if you get this far, lemme know what you think. And if you try the build, lemme know how you did!