I have a relatively mild but uncomfortable reaction to hair dye is there a product that will relieve the flaking & tightness of the skin?

I would take benedryl. Take it at night - it will knock you out. It isn't for tightness and flaking but since it's an allergic reaction, it might help stop the histamine response to the allergen.

Might be worth trying a dandruff shampoo - good for a flaky scalp generally, not sure if it will work or not. Or call a dermatologist - maybe they can give you a prescription. Best find out what you're allergic to as well - allergic reactions can get worse with each exposure, so you are going to need to find out what caused this so it doesn't happen again. Nothing to mess around with!

Sorry this happened to you - sounds like a very unpleasant experience!