Itching and scratching is usually a normal part of parrot behavior just as with dogs and cats. However, if the scratching is severe, constant and done with a vengeance to the point of losing feathers or getting skin sores, this may be caused by diet problems, dry skin, an injury, allergies, an infection (feather follicles can occasionally develop infections), or the pathogenic parasite Giardia. Your parrot should see a veterinarian to determine the problem as it could also be the start of a health problem or disease that could result in feather and skin destructive behavior.
While bathing is essential, if it is just dry skin, the best way to combat dry skin is with the addition of essential fatty acids (EFA-3) sprinkled on the parrot's moist foods - this includes help oil and flax oil. These oils can really help the skin and feather condition. The most common food allergies in parrots can be corn, wheat, soy, and peanuts - the base foods of most pelleted diets. Don't let the veterinarian push you into feeding a pelleted diet as these chemical-laden, highly processed foods may be the cause of the problem.