Only a few characters have kata videos: Kitana, Quan Chi, Scorpion, Frost, Kenshi (when you beat the game) and Blaze (when you finish Konquest with every character). I don't think there's any way to watch specific ones, aside from waiting at the screen that says press start, and waiting for the kata you want to see.

It will be cool if every character of the game had Kata, isn't it? Some with skills, other with weapons...