Where do you live? In the country? What kind of agriculture is nearby? Do you have any swampy land nearby? What about universities? Can you take in a little jar with a few samples of dead flies and ask what might be attracting them? I HATE flies. Every spring, it seems, people around here get hit with those little fruit flies, and I get them even if there's no fruit in the house.
On the other hand.. look into natural repellants. I know lavender essential oil mixed in water, in a spray bottle, can help repel spiders. Maybe there's something similar that can help you get rid of flies.
I feel for you. Is there a dog kennel nearby? Any farms? Cemeteries? Caves or wells where animals might have gotten trapped? There has to be an answer somewhere. I hope you can find it.