Ya'all are missing an important point, whatever your 'local' laws say chickens are, a Military Base is FEDERAL property. They don't pay local or state taxes on a base because of it, and they have their own Military Police force, local or state police and county sheriffs are not allowed past the gate without the base commander's permission.
Oh, believe me, I sympathize with the OP. I was a proud member of the military for 20+ years, but I did by best to live off base whenever possible. The convenience of living on base is a WONDERFUL thing, your neighbors are all incredibly helpful and sympathetic most of the time because you are all in the same boat together. When kids are involved, your neighbors all help keep an eye on all the kids, the kids are incredibly safe, and though nothing is perfect and weirdos are everywhere, there's usually so many 'eyes' watching all the kids, the danger is minimalized. Thing is, all the neighbors understand life as we all know it on the job... and when you're in the military, you are 'on duty' 24/7, even when you're on vacation (leave) you can be back to the job with a phone call, and you darn well better be able to be reached at the number you left on your leave form.
Civilians rarely understand the whole concept, but the Base Commander can walk in your door without knocking. He/she wouldn't dream of doing it, but it's always best to know that they CAN.