We have a fly problem too, but ours are very small fast ones, bold and curious, that drive me completely mad when I'm trying to cook. I have to cover up everything including utensils, and they get into the fly covers and lurk at the top where I can't see them.
Our compost bins are a distance away and I'm wondering if these little flies are associated with being close to cattle and/or horses.
We're thinking of getting some sort of electronic zapper - does anyone have any recommendations?