I also am in central Phoenix, smack dab up against a freeway. It is an older, mostly Hispanic neighborhood. So far, we haven't had any complaints, but I really don't have a lot of chickens and we keep a low profile.
Illegal possession of poultry is small potatoes in comparison to some of the other things that go on here.
We haven't had chickens in about thirty years, since we sold the family homestead. One day I was remembering how much fun they were.
The next day, my oldest son paid a call on a business near Pratt's. He stopped in there, and the next thing I knew we were back in the chicken business.
About a thousand dollars later, we had a chicken coop well concealed behind an eight foot wall. It is a real large back yard with mature trees and lots of bushes. It is a chicken paradise.
I don't know if the rooster crows or not. Who could hear it against the roar of the freeway.
Rufus