My Azrael is the "flakiest" little thing I have ever seen in my entire life, and she stinks and has Frito feet. There is no way I can get thru an entire week without bathing her. I've taken her to the Vet. so many times over this problem and all they can do is take scraping to test, put her on different shampoos and once gave her medication to take. Nothing!!! Now, I give her fish twice a week which I have noticed a decrease in the amount of flaking. I bake cod, salmon, perch or anything else I can buy or my husband catches in the ocean. She can't take fish oil. It itches her to death. Isn't that odd!!! I have also just ordered a shampoo that (someone that had the exact same problem with their dog swore by this shampoo) hopefully helps end this problem. If it adds to the healing process I can let you know if you want. I have noticed she doesn't itch if I keep her hair cut super short on her body. She is a cotton coat and it's extremely thick against her body otherwise.
I hope you can find a solution to help your baby. I know how worrisome it can be.