You would really only say she is in the kitchen. If you say she is on the kitchen it would mean she was standing on top of the roof of the kitchen. And you wouldn't say at the kitchen, for some reason you don't use 'at the' to refer to being in a particular room in a house. You could say, " at the bank" or "at the movies" but not "at the living room" and not "at the kitchen" hope that helps:)