I'm a fly control professional (an Independent Pest Control Operator).
While manure management is important, the truth is that the flies tend to breed in the first 2-5" of the soil. The life cycle of the various flies requires more than the coop floor can provide. Think about it- you would be able to see fly larvae/maggots if the breeding area was in the coop.
The simplest means to begin controlling fly issues is to apply Agricultural Lime to raise the Ph of the soil to 6.8-7.0, if possible. Flies require an acidic medium for successful breeding. Determine the Ph and apply the necessary quantity of lime. This will be an annual chore that is well worth the effort. Your birds will enjoy healthier and more nutritious grasses as a result of this simple fix.
If the issue is to the point of "Wow, look at all the flies", I would recommend Cyflutrhin (Tempo Ultra WP made by Bayer) applied to the exterior of the coop. Cyflthrin has excellent "knock down" properties. Generally, the flies prefer to be in the sun and don't care much for shade. Following the directions on the label, treat the west and south sides of the coop where the flies congregate. Cyfluthrin is also very effective on mites and lice. This is a safe and proven insecticide that has a very low toxicity for people, pets and livestock. The chemical has a finite life- about 30-45 days- it will degrade quickly and leave no residue in the environment. If used, simply allow it to dry completely before allowing the birds in and around the coop.
If you are more patient in your efforts, you could use a natural control mechanism. There exist many insects that are fly predators (use that as a search term). These predators, consisting of natural and indigenous species of flies and very small, non-stinging wasps, can be purchased online very easily (the species vary depending on one's geographic location). This mechanism of control will take a year or so and must be repeated annually. I have used this method for some of my clients that have a desire for a more organic means of fly control and it really works.
Good Luck