Rubbing hair off to the point of skin irritation is not a normal reaction to flies. She potentially has something else going on, such as lice or mites. You can see lice, at least. Use a nit comb and take a very close look. Mites need a skin scraping to see. You can do it if you have a microscope, if you don't, then a vet can do it.
If you still think flies are an issue, then you need to repel the flies. There are some essential oils that you can mix up that somewhat repel flies. But they aren't as good as a permethrin based spray. Look at the feeds store for fly sprays labeled for horses, they work fine on goats.