That's the same sort of rule we have here. (and we used to live in Ft Campbell and considered staying in Clarksville after I read they had the same sort of chicken rules as home!)
Basically, do what you want so long as no one complains. The biggest thing is to talk directly with the people it may affect, your neighbors. I did every house who's lot touches ours, 6 total. Easier when it's just two, but we're the deepest lot on this city block and so everyone around can see what we're doing back there.
3 little laying hens is totally different than a yard full of stags tied to barrels. An unwritten rule of sorts is no rooster, someone will complain. Maybe the person working 3rd shift, maybe the person who can deal with dog barking but not rooster crowing.
We have to put the chicken waste into a sealed container. So near the coop I have a large garbage can. I clean the coop "scoop" style, easy with pine bedding. The scooped stuff goes in the can, the bedding goes to compost as needed.
Check for supplies at TSC or Rural King. You'll need a horse stall refresher, like Sweet PDZ or Stalldry. Does wonders with odor while saving on bedding expense.
DE "Diatomacious Earth", food grade (powder type only!) works by killing anything with an exoskeleton such as bug larvae that may be in the runs or where ever. Liberal use of that is a life saver too.
Check out the visibility of your yard. Consider a privacy fence if you don't already have one. It will buffer some noise and keep them from being visible several houses down.
When I was evaluating the suitability of this specific house, I sat on the porch and I listened to the neighborhood noises when we first moved in. Traffic sounds from the semi busy road. TRAINs, screaming kids, screaming couple in the corner house letting everyone know their business. Barking dogs, more screaming kids coming through on bikes. ANOTHER train (we live near enough to the crossings to hear all 5 of them!!!). The idiot dog 5 houses up, it must be chained or left out too long.
And then I heard it. BuGOCK! Chickens! Already in this neighborhood! Faint, compared to everything else I heard. Off to Lowes we went for building supplies and I had chickens that week. Later we added ducks, the quack blends nicely with everything else, after 1 year with them, you'd miss it if it wasn't there.
In the morning when all is quiet, birds are singing, a couple of muffled quacks.. the only disturbance would be a rooster crow, it would shatter everything.
2 of our neighbors know the other people with chickens. The old man watches the ducks from his back yard. In the back, none of those yards are fenced, so 3 of those neighbors have all talked to me and 2 buy eggs. Next door on either side they like it. 2 on the far right don't mind and also don't care. 1 is unaccounted for, I think they're really old and wouldn't hear much anyways, they're never outside.
Might be different in a neighborhood that doesn't have a whole lot going on. Here... they blend, and are the least of it.
You can also conceal the coop area with landscaping. Anything pine will stay green year round and buffer noise and the visual. Bamboo too, but that stuff gets TALL. Grapevines, sunflowers, lattice type decorative fencing. Seems everyone is surprised when they see a cute coop, they were expecting something less... appealing? when they first see what you've built. All our neighbors except the 2 who are friends with the other chicken people did have some trepidation about the idea. Easily convinced though, and we've been good to go for 19 months now.
With how hot it gets down there, you'll want shade around the coop. But it's totally doable, depending on your neighbors. Even where laws are more lax and there isn't a lot of restrictions, one bad neighbor can ruin that too. So talk to them, they have the say-so.