What kind of brush are you using, and do you brush him on a regular basis? Beagles are usually not subject to matting, especially if they're brushed at least once a week.
I'd suggest a comb to get any matting out, then brush him weekly with a Zoom Groom rubber curry.
Dry flakey skin can have many causes, and diet is certainly one of them. But so is inadequate coat care, shampoo residue left on the skin, and parasites. One parasite, a mite called cheyletiella, causes a condition called walking dandruff. These mites are microscopic, so you need a vet to diagnose them. They're easy to kill with flea shampoo, though. Low humidity can dry the skin and cause flaking, too.
I wouldn't suggest adding any supplements until you've had a vet rule out other causes.
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