"Some dogs benefit from omega-3 and omega-6 fatty acid supplementation. Vitamin A administration at 10,000 IU orally once daily has also been helpful to some dogs. "

another vet site:
"Some dogs benefit form shampoos – especially keratolytic or antibacterial shampoos are helpful in mild cases. Topical propylene glycol (50 to 75 percent) diluted with water is also effective to decrease the scaling. It is used as a spray once or twice daily. Soaks with baby oil have also been reported to help in severely affected dogs. Dogs need to be shampooed several times to remove the oil from the skin.

In addition, some systemic therapies include supplementation with fatty acids, evening primrose oil, Eicosapentaenoic acid, and Vitamin A.

Drugs such as retinoids and cyclosporine are used in refractory cases."

The retinoids look potent and dangerous. I wouldn't go that route unless no choice.

This really looks interesting if you want to try an alternative. Heigh ho, heigh ho, it's an alternative way we will go.

Sorry for the bad Snow White take off.

Evidently, this is an autoimmune disease. Another thing you might try if you want to do the research is find out what the optimum healthy diet for a dog is and carefully feed your dog that way. What I think of commercial dog and cat foods is unprintable. I do feed my cats commercial stuff but I try to give them the kind that has more in it of what their bodies need. The ultimate for a cat is fresh kill (ackkkkk). Too many cat foods have other crap listed as their first ingredients instead of meat.

I've had psoriasis for years (autoimmune disease with scaly skin patches of cells that grow too fast). Dermatologists have ignored me but my psoriasis responds to a diet of lean meats (best is fish), fresh veggies and fruits, grains, healthy oils (i.e. Extra Virgin Olive Oil), a Mediterranean type diet. My psoriasis has improved over the years and disappears completely when I'm on the above diet and don't vary from it. You'll have to research diet for dogs.