If you are really struggling against assassins you can get Rageblade second and then build Zhonya's Hourglass third (you still get W evolve) and sit on a Dagger just to get your E evolve. It’s a huge early-mid game spike for Kai’sa. Some people play this way, but I personally think Q evolve is too important to delay like that.
If you don’t buy Pickaxe after your first item or you sell your Doran’s Blade you will delay Q evolve until you finish Rageblade. If you take Nashor's Tooth instead, you spike earlier with all of your 3 evolves, but only IF you buy a Pickaxe for Q evolve. If you build Guinsoo's Rageblade second you will get your W evolve in the mid to late game. You ideally always start with Doran's Blade. There are two ways to go about it, generally speaking: Rageblade 2nd or Nashor’s 2nd.