This disorder is the production of large or small scales/flakes of dead skin peeling away from the outer surface of the body.
We should keep in mind that dandruff (scurf) may be an indication of some underlying problem for which you need to seek professional advice.
Before seeing a professional you could safely try one of the following remedies which often solves the problem.
If your companion prefers the cold and has a dry, scaly and reddened skin and is also very prone to infection, give Sulphur 6c or 6k, 3 times daily for 2 weeks or a bit longer if necessary. Stop giving the remedy when you see a distinct improvement.
If, however, your companion prefers the warmth and has a dry, rough, scaly skin and the flakes of dead skin are white and (often) small, give Arsenicum album 30c or 30k, 3 times daily for 8-10 days and repeat after 10 days approx. if necessary.
If these remedies don`t act properly you should see a qualified professional for full case taking, because skin problems are very difficult to treat properly online.
Wim P. /William