I have no experience with chickens and fleas...I do however have experience with very small kittens (3 weeks or less) having infestations! For our flea-covered kitten, he was too small/young for the flea dips, so the vet had us try Johnson & Johnson baby shampoo (the original yellow one, you can find it at Dollar Tree). We gave him several baths with that and it helped, but didn't rid him of the fleas. After about a week of twice daily J&J baths, we switched to Dawn dish soap (the original blue). Thick ring of soap around the neck, just behind the ears and then work from the tail up. The fleas will try to flee the soap, but will run/hop right into it at the neck line. After one bath, the fleas were nearly gone! After a second bath, they were completely gone!
I assume, since the blue Dawn is safe for wildlife cleanup (it's how they get crude oil and such off wildlife) that it would be a proper item to use on a chicken as well.