The flax you are talking about is that flax seed oil?????? Because my vet had told me to put Rocky on it when his skin problems began, and he is still on it!
Flax seed oil is not all that good for your dog and downright bad for some dogs.
The following is sourced from here: The Number 1 Reason for Excessively Flaky Pet Skin
It says flaky but it really covers your problem too.
"Most foods available, whether purchased commercial or homemade, are rich in omega-6 fatty acids. Because the average pet diet is heavy in omega-6’s, supplementing with additional omega-6’s in the form of corn oil, olive oil, safflower oil or even flax oil (that contains some vegetable sources of omega 3’s, but also omega 6’s) can create an imbalance serious enough to cause skin problems.
Omega-6 fatty acids, in abundance, become pro-inflammatory oils. If your pet gets too many of these without a balance of healthy fish-based oils – DHA and EPA – it can be a real problem.
It’s also important to note that dogs and cats can’t convert omega-3 vegetable sources into DHA. Flax oil has some omega-3 value for humans, but that doesn’t hold true for your pet. So it’s really important that you supply fish-body oils or krill oil to your dog or cat. Algal DHA is also a good source of omega-3 fatty acids."
Try putting her on a premuim food such as Acana Pacifica which is a grain free 60% fish dog food kibble. This is, imo, the best fish based dog food out there for the money. Champion Petfoods | ACANA | Products - Puppy Small Breed
Or you could go with California Natural line of allergy foods which have a very limited ingredients.
Another helpful source: http://www.k911.biz/Petsafety/Licking.htm