Flies are horrible here too because it's been so wet. I don't know dairy goats. We use to milk cows and bedding is very important to dairy animals to prevent udder injuries and mastitis.
Flies eggs generally need moisture, so technically it shouldn't be the dry bedding causing problems.
How...
Sounds like the only place flies can breed is in your deep litter or under the stall matts.
Have you looked under them? Deep litter is a perfect place for flies, we clean ours out in the warmer weather.
We don't provide bedding this time of year. My goats prefer raised wooden platforms for...