I've lived in Richmond, VA & Western Henrico Area and know a little history and facts.......Henrico is a county the far east there are farms but the west end of Henrico Urban sprawl has exploded in fact Short Pump Mall was built recent knocking out an old farm..
There are pocket farms all throughout West End Henrico and are grandfather claused as well as in the fan district of Richmond where I grew up via Virginia state law ~ can succeed county zoning laws this is how! the livestock or farm operation must be historically present before development and on-going without interruption for 6 months out of the year.
If there is no real farming or livestock on said area for over 6 months then a petition for re-zoning is done removing urban farming or keeping animals deemed livestock.
Re-introduce farming have two options: petition the zoning board with plans to ensure no residential nuisance doctrine prior to re-introduce livestock or farming.
Second is wild life/park free roam of animals deemed livestock. Animals like Canadian Geese are wild and protected if domesticated ducks roam freely even origin domestic and a public municipal park shelters wildlife but can't disrupt wildlife to cull domestic without legal permit or recognized authority over wildlife.... Meaning most police/animal protection are not authorized to touch any wildlife unless rabid and public safety ......it becomes the Jurisdiction State & Federal Wildlife commissions or legal management authorities..........Hence Byrd Park in Richmond with ducks and the wild ponies off the eastern shore.....livestock left as free roam. Unfortunate, chickens don't fit the second area ---during the depression/victory garden era residents around Byrd park's shield lake kept ducks yet evaded demand removal under zoning via neighborhood politics.
I noticed you mentioned Farmington community of Henrico county so it's all neighborhood politics via the zoning.... Residential developments going up these days most have strict covenants to supposedly make for better neighborhood aesthetics therefore increasing property market values and hence assesses tax property values. These housing covenants are spilling over to older homes built in the area via re-zoning petitions on the premise of property values.
You have to look at your home when was it built can it be deemed historic as there is a little thing called heritage restoration but done or permitted if you plan to submit your home for public tours/community events that support (interests of historic preservation, public education or non-profits that support human or community welfare). It usually, means your residence must be built before world war II. I currently live in the Brookland area Henrico, there are pockets of houses among new sub-divisions that still have horses and use wells for a water source other then new building codes for use public annex municipal of Richmond.......
Why property transfer under 6 months or during vacancy livestock or original farm operation remained.....one sold recently and they made a petition to return to old permit livestock animal in authorized the condition of advertised sale feature property with horse barn.
Currently, there is a war over land development throughout Virginia farming falls under a business operation therefore pre-zoned for industrial economic or other form commercial development. Yet also a residential zone as many residents rushing the remove pre-zone business consideration allowance for industrial or commercial encroachment in a resident area. Once again this battle is neighborhood political based off nearby housing sub-divisions imposing the sub-divisions development plan and dictated under property value interests. Your real fight is "Attractive Nuisance Doctrine" find state laws that have out won local codes that have weight of law in Virginia or the county Henrico must define/conditions warrant word "Nuisance" and prove you've created a Nuisance!
Best bet re-petition the board draft written plan per-use and prove no nuisance - it must state personal development and enjoyment residence not influence economic/business rezoning upon a residential zone, must make public the guidelines or your preset intentions to remove all possibility there is no nuisance ( such as containment, removal waste or health issues, the coop construction blends with area structures, noise abatement or etc). In others words bring strong argument and proofs or condition also list any operational county codes permitted in zoned areas/ state codes as well as federal defining hobby from commercial interest or even elaborate/exotic pets some times rare breeds apply especially preservation distinct towards U.S. or place of origin some under federal agricultural/education/preservation laws......as there are loopholes legal ones. Your real fight is the resident to business boundary as even operating a business from home in Henrico county is getting harder---imposing new restrictions every year then commonsense zone guidelines.
Normal these issues don't make news till neighborhood politics or a traffic by-passer get involved so you have a neighbor that just hates your chickens 99% time is bird poop on the car or a speeder that cuts thru. There were chickens roaming the street currently live, didn't mind but real issue removed rouses with dogs, cats, annoying kids, and misplaced blame via blue jays and mocking birds. Only one over zealous commando vegan eating animals are cruel!
As far annoyance actual roaming the street per traffic in a residential area (yes the escape just as any pet) hint: proof neighborhood safety ---really didn't mind as kids play here they did a much better job then speed limit signs 25 mph as yes now gone daily folks cut through to access interstate drive past at 45 mph to 75 mph some times with kids on bikes or skate boards not caring potential rolling a child across their hood. There are occasions I deliberate had to drive around the block to play road hog slowing them down even just after dropping kids off from school......there are real aggressive acceleration after passing school bus or active school zone limit!! especially near interstate/highway areas. In past dead chickens on the road pending dragged breaking proved high velocity speeding and evidence police patrol instead it went the other way.