How many times do we have to repeat it: There is no such rule!
They bylaws are silent on flag-flying!
Anyway, if YOU people did a little more research YOU would find that other homes in the neighborhood have the short staffs attached to porches that fly flags. Apparently there is nothing that prevents our hero from flying an American flag if he used that type of support for it. Or, at least it would eliminate the HOAs given reason. He moved to a place with a HOA and got hosed. Sucks for him, but thats his problem. And its not news..