Try BREWER's Yeast instead. You can find it in pill form at Pet Stores. You can also find it at GNC for the powder form. Avoid the kind with Garlic if possible. Gives them gas.
The Brewer's yeast helps with fleas, coats, and skin. Expect it to take a few days to get into their systems. It gives off an odor that humans can't smell but the fleas can. They don't like it and will get out eventually.
I am worried about the Zinc. That is a metal. It may be causing the hair/skin issues. I have always heard that high zinc will cause baldness.
I also recommend using a brush often and bathing to once a week or 2. Excessive use of shampoos can irratated the skin as well. Some diseases of the skin are "Catchy" so if one has it BOTH will get it.
Good luck!