Some good ideas here, but I disagree with the last suggestion to use flea products on your cat. I learned years ago that a daily combing with a flea- or fine-tooth comb keeps fleas away. Plus, my kitties LOVE being combed, Andy demands it several times a day.
My first kittie had a ton of fleas…a bath fixed him right up. Followed by daily combing. Not saying he loved the bath, but it had no side effects.
Our cats also like to be combed every day. And as an added benefit, they NEVER have hair balls.