thyroid test performed. It's possible the thyroid level is on the low side which would explain the flakey skin.

If allergy as in a lot of scratching then 1-2 mg/lb of Benedryl at the peak of the allergy season will help.

Probably is best to avoid any supplements that contain Vitamins if they are to be administered in large dosages. There are more than enough straight fish oil supplements that will help due to their containing Omega-3 fatty acids. Also a single dose daily of Vitamin-E 400 IU (succinate salt or dry form) will help the skin repair itself.