Fleas have an extreme vulnerability to anything with moisture-zapping qualities, which can badly damage their exoskeletons. One very effective flea-killing tool is table salt.
To get rid of fleas, grind salt into a fine powder and thoroughly rub it into any infected fabrics. Apply it evenly over carpeting and furniture and leave it on for 12-48 hours.
Flea eggs may still survive, since the salt has to make contact with fleas' exoskeletons to work. Do a salt treatment at least once every 1-2 weeks after your first one.