We used the fly traps last summer. I believe we collected all flies within a 5 mile radius as it seemed to attract more and made the problem worse. Additionally, the fly traps, while they work phenomenally, smell like death. You won't want to hang it anywhere near the coop or run.
Although we have deep litter, there are still flies. I pick up the poop laying on top every time I go out - numerous times a day and this obviously helps. With deep litter, there really is no bad smell but there is no way to totally eliminate the flies. We also have numerous fans running all day and this helps as well. Where there are animals, there are flies. Too bad chickens don't eat them, they'd have a smorgasbord.