I do know (from my own experience as well as careful label reading) that flies are not affected by permethrin, so K9 Advantix treatments won't help with those, although they do help with mosquitoes and work well for ticks.
The one time I had a really bad black fly experience was car-camping in Michigan's Porcupine Mountains in mid-June. It was a hot day, and the flies came in clouds! I finally put Hysson in the car, headed for the highway, drove fast with the windows open for 10-15 minutes to blow out the flies, then closed up, put on the A/C and didn't return to camp until dark. We left at dawn the next morning and didn't stop for the night until Fargo, ND.
I understand that there are repellents (not DEET) that will work specifically for biting flies, but make sure they are safe for dogs. Most repellents can only be used on places that the dog can't reach with her tongue, which severely limits their effectiveness. Talk to your veterinarian and read the labels. Please, let us know what works!
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey