I would have thought if it was strike you would have seen where the problem was on a goat, have you checked her over for wounds, maggots etc? Check out her feet as well, they can get strike between their feet.
I use spotinor on the goats, a pour on solution, but not suitable for milkers.
There is also a citronella based spray that keeps flies off.
Do you know what the flies are? Any chance of a photo?