Alice, there are quite a few causes of dandruff in dogs but the most important are seborrhea and, less commonly, the dandruff mite. Your vet can directly visualize this mite or perform superficial skin scrapings looking for it. Seborrhea is more likely and the "dry" form (seborrhea sicca) can appear simply as dandruff. Here's my more complete synopsis of seborrhea for you:
Clinical signs may include a dull, dry, lusterless hair coat, excessive scaling (dandruff), follicular casts, scaly and crusty seborrheic patches and plaques, and greasy, malodorous skin. Most of the body is involved to some degree, with interdigital areas, perineum, face, axillae, ventral neck, abdomen, and skin folds usually most severely affected. Pruritis (itchiness) is mild to intense, and ceruminous otitis externa (oily external ear canal inflammation) is common. Secondary skin and ear infections with bacteria and Malassezia (yeast) are often present.
Here's how you might address it...
1) Ensure good nutrition. A commercially balanced dog food that meets AAFCO requirements should be fed. You should find the AAFCO statement on the food label.
2) Any secondary bacterial and Malassezia skin and ear infection should be treated with appropriate topical and systemic therapies. Periodic treatments or long-term, low-dose maintenance therapy may be needed because these dogs are susceptible to recurring infection.
3) For symptomatic control of ceruminous otitis, long-term maintenance ear care is necessary. Ear treatments with a multimodal therapy (consult with her vet) or ear cleaner should be administered to both ears every 1-7 days to control cerumen (wax) accumulation.
4) For symptomatic control of seborrhea, antiseborrheic shampoos and emollients may be used every 2-7 days until the skin condition is improved (~2-3 weeks), then, bathing frequency should be decreased to every 1-2 weeks or as needed for maintenance. Antiseborrheic shampoos contain some combination of sulfur, salicyclic acid, tar, benzoyl peroxide, and phytosphingosine and can be found over the counter in pet/feed stores, online, or at your dog's vet hospital.
5) Daily oral fatty acid supplementation may be helpful as an adjunct therapy (180mg EPA/10lbs). EPA is thought to be the most antiinflammatory of the essential omega-3 fatty acids. It's plentiful in fish oil supplements.
6) Vitamin A 8000-10,000 IU per 20lbs orally administered with a fatty meal every 24 hours. Improvement should be seen within 4-6 weeks.
7) For dogs with severe, greasy, malodorous, pruritic seborrhea, treatment with systemic corticosteroids may be helpful. Acitretin (a retinoid) may be helpful in some dogs. Calcitriol (vitamin D) may be helpful in some cases.
The prognosis is variable, depending on the severity of the seborrhea. This is an incurable condition that requires lifelong therapy for control. Please respond with further questions or concerns if you wish.