Kai'Sa is a a high power dueling ADC that closely resembles Vayne in both play style and scaling. While ADC's in the top lane are not known for being great, the good range and high trading power of Kai'Sa are a good fit for the 1v1 lane.

It is important to start the game looking at which starting item you want. Most top lane match-up should be easy to farm in, so I favor Dagger so I can duel at lvl 3 and to shortcut the cost of coming back to lane with Recurve Bow & Boots. Trading is generally easy, AA and Icathian Rain make it easy to poke with and Supercharge + range make it hard to go for a full fight.

The best thing to do is push the lane for the first couple waves. You have better push than most top laners at lvl 1 - 3 and almost not one can fight you till lvl 3. at 2:45 begin to watch for the jungler. You are a nice squishy target and if either top lane or jungle has CC you will die. Void Seeker
Gives vision on its path plus gives true sight of anything you hit. You should use this to check river brush before walking down to ward it. Void Seeker has a long cooldown, so try not to use it to just poke.

For dueling in the early laning Your passive, Second Skin , makes you a very strong dueling champion. Procing it is the trickier part. Since it does percent damage based on missing health it making you much more deadly when a champ is low. As well Void Seeker has a high base damage, and applies 2 stacks of the passive, plus with its long range it is good for finishing off a champ that flashed away from you.

Once you get Killer Instinct, it get much easier to finish off those that run, but remember that a lot of top laners have powerful ults, so chose your timing well.

By mid game you should have Supercharge evolved and working toward Blade of the Ruined King. by this point you should be able to wander. With full stacks of Guinsoo's Rageblade passive and Supercharge active you have over 2.4 attack speed, making you dangerous to towers. This is the time to split push and Teleport to exposed towers. You should look for opportunities to pick off squishy or tanky members of their team by warding their jungle. As well, you clear most camps quickly, so that is another way to boost your gold and starve the opposing team. However, you are still squishy so try to avoid assassins (unless you can outplay them).

Once you finish Black Cleaver Icathian Rain will evolve and you should be able to duel about anyone, though you should still not face check a bush with an assassin in it. Black Cleaver is strong because with a full Icathian Rain volley you get the full armor pen. passive off.

There is not mush to say here. If you farmed well and got a few kills by late game you should be a monster. Between the high burst and percent of missing health on passive your end game looks like a Vanye end game. Don't get caught in CC and use invisibility to reposition. Remember you have Teleport , so you can split then join your team or use it after a fight to push toward the nexus (or maybe just backdoor a game with your high attack speed). This is the part of the game that is the most fun.