The fly predators didn't work out for us, because we're on a small lot and it appears that the horse farm 1 mile west blows them over. So we do traps for those that arrival, and prevent the breeding of them when they get here by picking up poo every day. We're restructuring the compost right now, cinder block on 3 sides, so that there is less of a cool edge to it. If compost is working right, it's too hot for flies to breed in. Too cool, plus moisture, fly haven.
Having sand as the bedding helps because it dries the poo faster than other bedding types. If you ever watch the flies, notice which poo they go for. You want that stinky stuff dry ASAP to prevent the flies. (they like the super stinky wet ones the best, I'll hit the whole mess of it with a swatter if I see a pile of flies on it out in the yard)
Hanging vanilla scented car fresheners in the coop keeps the flies out of there.
DE, stall dry, and Sweet PDZ are all helpful for odor control and drying the place out.
Really though, staying on top of the poo helps the most. The traps work second best, but they can get bogged down quickly if the flies are breeding nearby. We have 3 traps going at all times, spaced out.
It's been less and less of them every year. Way better than more and more!
Wish all the neighbors would pick up after their dogs too. Lot's of dogs. We have a sealed bucket for putting dog poo in, and we toss it. They create too much for the compost pile to handle. Last year I hunted all over for breeding sites and couldn't really find anything. Tore apart the compost looking for them. Seemed like they were hatching elsewhere and coming over, so we're stuck with using the bag traps. There are 3 horse barns within 3 miles, all west, so they can blow in easy enough.