cat with dandruf i cannot cure

[tea]

I have a 4 year old male black cat that has terrible dandruff on his
back. It's only from about the mid-shoulder back to his tail. I've
bathed him once with an anti-dandruff shampoo but with no lasting
results. My vet doesn't seem concerned about it and told me to brush
him more often. When he was around 2 years old he accidentally knocked
over a burning candle and hot wax covered his back, the same area he
now has dandruff on. I ended up having to use electric clippers to get
the wax off him. He has a thick double coat, dark black with a gray
undercoat. He did have the dandruff prior to the candle incident but
it seems to be getting worse as he ages. I have him on a high protein
diet as he was overweight but he's now slimmed down though not what
I'd call athletic. I live in a small one bedroom apartment and this
cat is strictly an indoor critter.

Any suggestions?

[Chameleon]

I was wondering if you give him flea medicine in that area? Maybe not
since he's indoors but that's the same area. Most cats cannot clean
that area. I am sure they are so many natural things he can eat for a
better looking coat. Good luck. Keep us posted.