Chickens? Isn't that against HOA??? WOW
From the City Chicken the laws for Fort Worth.
Fort Worth, TX. Can have up to 12 chickens within the city limits on a residentially zoned lot. They have to be in a chicken coop and the coop has to be at least 50 feet away from any house. That includes your own house and any neighbors' houses.
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You should call animal control again, and city code compliance as well. Farm animals are a different deal than just letting your dog get out of your back yard. There are health standards to deal with as well. Some lots in the far corner away from the house *might* meet the 50' requirement, but I doubt it would be 50' from the neighbor's house. If I wanted to live on a farm, I would have moved out to Parker county.