Absolutely and the cats I have catsat loved it on their food. Tea tree oil is something I use for fleas/ticks. I put it in their rinse water. I also like Petguard shampoo (unsure on your kitten's age and if it is appropriate for her) because it has pennyroyal oil in it which also helps deter fleas. There is also Halo brand Cloud nine herbal flea dip. I've never used it but all their other products I've tried have been amazing!
When and animal gets fleas, it means it is dirty (not necessarily unwashed which can be part of it but malnourished). Most kittens and puppies are. To really take care of the problem long term, I totally recommend a high quality cat food (like Wellness, Innova which is high in fat though, Wysong, petguard, solid gold, etc.) What you pay for is what you get to a point with high quality foods. Maybe a pet supplement too. Flea season will end soon, so just try to get through this season and with a high quality food and using a natural flea deterrent shampoo (or adding tea tree oil to bath time), next year shouldn't be as bad.
A word on Advantage, I strongly do not recommend either that product or Frontline. My direct experience with it was with my pom mix. When I brought him home from the shelter, I noticed that where they gave him an application (and it is unsafe for pups and kittens to, btw), his skin died and turned black.
As far as your house, if you have kept the kitten in the house at all or plan to, just vaccum all carpet areas and rugs (something we all do anyways and when Kipper had his flea problem when we first brought him home even after a chemical flea treatment, I figured a couple extra times won't hurt.)
Last flea season, we were in the same boat with our little guy, but not a flea this season (or tick). Diet is a big key.
Jenn