Why does my dog have dry flaky skin?

I would first rule out any infection or parasites by going to the vet and doing a skin scrapping test and blood tests. If they don't find anything, you can also go see an allergy specialist and make sure its not allergies.

If the problem really is dry skin and nothing else, adding a bit of coconut oil, fish oil or wheat germ oil to their food. For allergy prone dogs, feeding a raw diet or at least a grain free dog food really helps.

Adding a small drizzle of olive oil to your dogs food can help to moisturize the skin.

It could be allergies, or it could be parasites, or a disorder like Cushing's disease or hypothroidism.

To help a dog with allergies, try to wipe the dog's paws after every walk (no soap needed-just a soft wet towel or cloth-or with dog wipes, which aren't as harsh as all purpose/cleaning/antibacterial chemical laden household wipes). Also, brush and groom regularly to remove dirt and debris. And keep the home as clean, dust free, flea/insect free as possible. Basically, avoid or limit exposure to allergen, control the symptoms (itching, dry skin, etc.),and if needed consider immunotherapy options, such as allergy shots. Ensuring a high-quality diet (free of common allergens such as wheat, corn, soy, chicken and more) and adding a humidifier may help. I'd also suggest keeping on parasite preventatives.

Parasites, infections, and systemic disorders will require a vet's care.