The following link explains the regulations governing importation of birds into Florida:
http://www.doacs.state.fl.us/ai/faq/idcapbif_faq.shtml#q10
In addition to a health certificate from a vet, you would have to have a specific test done for the presence of disease in the bird. It may be too much of a hassel to go through. Additionally, chickens are subject to influenza, colds, and infectious diseases that could more readily attack a bird that is stressed from an airline flight.
Should you decided to go through with transporting them, you might check with the airline. Most airlines allow small dog/cat carriers that fit under the seat to ride in the cabin with you, I don't know if they would allow birds.
I wouldn't do it if I were you.