If I were a chicken breeder in DeKalb County, Georgia, I would organize a "Chick-In".
First, identify who your problems are. The people making the decision to not allow chickens need to be singled out and popular public opinion must be organized against them in a fashion that will make them cave in to your demand, rather than face the backlash for their stance against chickens and more specifically, small business owners and farmers.
The problem is that your politicians have been allowed to control the dialogue and paint this out as them preventing your neighbors from having noisy chickens. You need to change this dialogue to paint your politicians out as being anti-jobs and pro-big agriculture, which will turn voter opinion against them.
Second, identify your local allies. If you have animal rights groups in your area that will help support you, great. If not, there is still a lot you can do by yourselves. Utilize social media and if you can, get news coverage on the situation to increase pressure on your politicians by shamelessly pandering to animal lovers, showing your chickens to the public and thereby increasing the sympathy factor in your favor by informing the public that your chickens have names and are friendly, family pets.
This is especially effective if you happen to have children.
Could you imagine the public outrage and backlash caused by having to tell some cute little kid that they might not be able to keep the family pet because of some evil, greedy politician who only supports big agriculture and hates small business is generating revenue for the county by preying on some defenseless mother and father trying to put fresh eggs on their table during tough times for their children and charging them outrageous fees simply for daring to provide for their family?
Organize a public protest with your chickens. Do you really think that animal control could handle several hundred chickens or that the local police would really bother you with anything more than a fine that you can then use to show how your local politicians are hassling peaceful protesters? Oh, the humanity of it all!
Face it, they can not really do anything to your or your chickens and if they do, you have created the perfect grounds on which to cause some legal trouble for them and I guarantee that you will have lawyers just begging to take your case for free because of the potential payday. Better yet, do you really think that your county will want that kind of legal attention and the resulting negative publicity? They would rather cave to your demand at that point.
By the end of this, you will have them singing the praises of chickens and trying to spin their new decision to allow them as "progressive change" with the times and a "pro-small business" decision.