Phyxius
Zoooooooom
Are you talking about the house flies or the tiny black flies about the size of a large gnat?
Stable Flies are often called biting house flies. They look very much like house flies however, house flies don't have a mouth capable of biting like the stable flies. If you want to get technical about it their name is Stomoxys calcitrans and they are one of the species of biting flies that are "prey" to fly predators. Horn flies and black flies which are also annoying biting flies, are also susceptible to fly predators.
Do you perhaps mean midges (Culicoides)? Around here they're also called no see-ums. Many horses, especially those from cooler climates have sweet itch which is an allergic reaction to the saliva of biting midges. My mare has sweet itch, it sucks