Here's a not nice tip (for me, it wasn't, but it worked), but my mom gave it to me when I adopted my first kitten, and he had a lot of fleas.
Firstly, use liquid dishwashing soap (yes, using this is really weird) and put it all over his body, the fleas die immediately. Since he is a kitten, he can't be medicated or put on flea powder yet. Just clean the kitten well with warm water and remove all the liquid soap. I recommend putting it around the neck first so they don't get on his head. And give him a quick bath.
After that, you need to fumigate your house, but that is dangerous for the kittens. So they should be somewhere else.
This is the only way I could get rid of the pesky fleas.
Honestly, none of the methods the vet recommended worked, just what my mom told me.
I read about dishwashing soap too but was hesitant about using it. But I am willing to try because the poor kittens are fighting for their lives. I wonder where they hide tbh, my kitten roam around in a lot of places and we normally don't have too many furnitures or sofas. What do you use to fumigate your living areas?
We hired an expert to fumigate. He used a chemical that was good for the environment and not as toxic as others. I don't know the composition.