Hello and
Who has to prove that a domesticated or tame animal is a pet? And how?
Are there any specific rules for defining a pet by anything other than species?
By such standards, if an animal must be proven to be a pet as judged by its behavior/reactions to humans, many dogs and cats are not pets since they're unfriendly even to their owners or most family members, or just aloof.
Do you have any specific code you're trying to comply with here, i.e. rules utilized in discerning livestock from pet based on what? If it's as simple as ticking the boxes so to speak you should win but most regulations simply decide some species are pets and some are not, and that's that, or they have ridiculous regulations as regarding keeping the animal, i.e. in Australia in Queensland you can legally keep five or more large horses in the space you are required to have for a single sheep. Priorities, and financial incentives.
I hope you succeed, here, certainly enough people are in the same boat as you are and working hard to change the rules. If they are responsibly kept I don't see how they're any worse than responsibly kept dogs, cats, or whatever. You can catch diseases/parasites etc from all of them, it's not like chooks are extra dangerous.
The biggest obstacle is public perception, as your neighbor is likely being illustrative of; many people will let their dog poop on others' lawns, let their cats urinate in others' areas, and still feel that chooks are degrading the tone or value of the neighborhood.
There's ignorant and strong prejudice against them with little in the way of facts supporting the stance against chooks. Public awareness of how quiet, clean, and non-stinky they and their living quarters can be would help. As always it's those who fail to attain and sustain such standards who give the rest a bad name, but hey, that hasn't gotten dogs or cats banned from suburbia, has it?
You could try a community petition, or something similar, it has worked for some. In some areas some breeds are classed as pets or cage birds, i.e. in Australia in some places Silkies (even roosters) are/were able to be kept in suburbia because they were classed as cage birds... Though I don't know if that still stands, it's old info now.
Best wishes.
