Hi,
I just had this problem with my puppy. I bought Salmon oil from Pet co and my vet recommended Tropiclean Oxy med oatmeal shampoo and also the rinse. You can also buy this at Petco. Expensive but well worth it! Follow the directions and leave both shampoo & rinse on for at least 3 minutes each. Make sure to rinse her well! His skin problem is now gone. After baths sometimes they'll be a little flaky because you washing off the skin that doesn't come off much like other dogs. Puppies usually have more dry skin also. That's what my vet told me. Good luck.