I used to think exfoliating your scalp was a myth invented by fancy salons. It’s not. A gentle physical scrub (like a soft silicone brush) once a week can remove dead skin cells and stimulate circulation.
Just use it in the shower with your shampoo in gentle circles. Don’t rub raw. You’re not trying to sandpaper your head. If it feels aggressive, stop. Your scalp is not a kitchen counter.
Another option: a gentle acid toner (like salicylic acid in a low percentage) on a cotton pad, dabbed onto the parts that flake. Do not do this if you have open scratches. Your scalp will revolt.