I wonder what you do with the manure once you take it off the poop boards? Is it just dumped someplace or buried? I have found that when the chickens can access their droppings the number of flies diminishes to the point where they aren't a problem. Like it or not the birds will sort through the droppings to get the fly eggs and larva. I don't use poop board but put down a deep layer of pine shavings and clean the coop once a year. In 25 years of keeping from 20 to 40 birds I've never noticed a problem except in the early spring after I've cleaned the coop and haven't tilled under the droppings. This goes away as soon as I either till the garden or let the chickens out to dig around in it. Otherwise, living where we do in the country, the only flies we have problems with are black flies and horse flies.
BTW, while using vanilla air fresheners will drive the flies out of the area where you hang them, they'll just go someplace else.