Hi! You didn‘t mention if you‘d considered the food aspect ? Grains, some sorts of meats (e.g. chicken) can be responsible for skin problems, as can a lot of the ingredients that go into some treats, biscuits , chews etc. If he does infact have an intolerance/allergy, then no matter what other supplements you give him, the cause isn‘t being eliminated.
I realize a raw or even a DIY cooked diet isn‘t for everyone, its a bit more time consuming for one thing, but it might be worth giving it a try, keeping ingredients simple to start with and then introducing other things one at a time and making notes on the reaction. There‘s a mine of information online, including a good facebook group for raw feeding. (You can also cook, if you don‘t fancy raw)
Perhaps make a list to consider
anything at all, however small, that could be causing trouble i.e. washing powder/ softner used for bedding, shampoo, air freshners, etc etc and then try alternatives while keeping a sort of diary to monitor reactions. Is it worse in the winter? Could the air in your house be dry? (i have a problem with that). I think I‘d try a process of elimination before giving supplements though as, if it is indeed food related, you could end up in a vicious circle, a normal healthy animal on good well balanced diet shouldn‘t require much in the way of supplements.
Last thought - could it possibly be a form of stress or even boredom?
Hope you find an answer !