I would suggest buying a flea comb, and then combing as many of the fleas off as you can. Have a container of warm soapy water next to you while doing this so you can drown the fleas as soon as you catch them. This is your safest option at the moment, and will provide some immediate relief for the poor kitty.
There are also some medicinal flea treatments, but I cannot tell you how safe they would be to use on a young, sickly kitten. I'm sure someone else can offer some good advice in this area. Be careful about using OTC medications, as some can be dangerous and cause serious risks even for adult cats.