I don't understand the issue with flies being related to FF. Is your run bare ground? I'd more likely guess that the flies are breeding in the poo, and just attracted to the FF. If the feed is not left out for more than 24 hours, the fly maggots wouldn't have time to mature, therefore, any eggs laid in the feed would be eaten. I feed twice/day, and the feed bowls are usually scraped clean twice/day. If your FF is left open to the air, no covering what so ever, perhaps that might be a bit of an issue, and you could cover it with a top to allow air exchange, but exclude flies. Are you actually seeing maggots IN the FF???? You might consider putting a deep mulch in your run, if it's bare soil. That should attract plenty of beneficial organisms to help rid the area of flies.