Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your dog has developed dry itchy, skin and I understand that you are what you can do for him.
Dry skin in dogs is usually related to either a poor diet lacking in protein and omega 3 fatty acids (very unlikely if you feed a good quality commercial dog food) or an underlying health problem that is affecting his skin health.
If your pup has any fur loss of very scaly dry patches and hasn't had these areas tested to look for demodex, sarcoptic, or cheyletiella mites I highly recommend that be done. These mites can lead to hair loss, increased skin scale and secondary bacterial infections which are itchy.
Your pup should also be checked for ringworm, which is a fungal infection. We see this more in cats but a weakened or immature immune system can allow the infection to thrive. Ringworm spores are quite hardy and are found in the environment.
Dogs with low thyroid function also have poor skin health. If he is overweight without eating a lot, and/or seems lethargic compared to other dogs of his breed hypothyroidism is possible.
Allergies, both to flea bites and inhaled allergens, are another reason for itchy skin.
One thing that you can do now to improve skin health, reduce the itch, and will help support a healthy coat as well is to add an omega 3 fatty acid supplement. I like 3V caps or Derm Caps. I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give 20mgs of EPA per pound of body weight per day. For example an 8 pound dog could take 160mg of EPA per day.
Cool water baths with an oatmeal shampoo or chlorhexiderm shampoo (which is antibacterial and antifungal) and a conditioner with an antihistamine may help. The water rinses off allergens and the cool temperature soothes itchy skin.
If you aren't using any sort of flea control you should be, especially this time of year. You can use an effective topical like Advantage II or Frontline Plus monthly. The Seresto flea collar is another excellent option and has the benefit of 6-8 months of continuous protection. It is the only effective flea collar safe for cats and dogs. Most of the flea preventative products available over the counter just aren't very effective and I would not waste your money on them. All pets in the home must be on flea prevention or the ones not treated become a flea reservoir.
Best of luck with your pup, please let me know if you have any further questions.