Can this thread be updated? http://www.backyardchickens.com/a/jacksonville-florida-chicken-ordinance
Sec 656.422 was updated in June of 2015 to allow backyard flocks in non AGR/RR zoned parts of Jacksonville, FL. Please note, the beaches have different zoning regulations, though there is an effort underway to update ordinances there too.
In short, you must be zoned single family residential and attend a class at the Duval County Agricultural Extension prior to applying for a one time $25 permit to keep a flock of 5 hens. There are a list of rules and regulations around your coop setup. By applying for the permit, you acknowledge you'll consent to a noticed visit from Code Enforcement if a neighbor complains you are being irresponsible. There were also non HOA neighborhoods opted out. If you live in a HOA or deed restricted community, check the rules first as these rules supersede city zoning.