From the VCA Hospital website
How do I prevent fleas on my kitten?
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No matter where you live, fleas may be a threat to your kitten and to your household. Fleas spend a short time on your kitten and then venture out into your home. Adult fleas feed on the cat’s blood, then hop off their host to lay eggs in the environment. Eggs hatch and the emerging larvae live and feed in your home. Larvae mature into pupae which lie dormant in your carpets, furniture, and floorboards. The pupae eventually hatch into adult fleas. The entire flea life cycle can take as little as 3-4 weeks under ideal conditions; in unfavorable conditions, the cycle can take as long as a year. Therefore, it is important to kill fleas on your new kitten before they can become established in your home.
Many of the flea control products that are safe on dogs are dangerous for kittens, so consult your veterinarian before choosing a flea control product. There are many safe oral and topical medications that control fleas, treat intestinal worms, and prevent heartworms . These products are administered once a month, even in young kittens, and will protect both your cat and your home from fleas. Newer flea prevention products last 3-8 months.