It may not be an allergy.
I've seen that kind of skin in several fosters, esp. in the back area just above the base of the tail. There are big flakes of skin or scab bits that show up in the coat in that area. As soon as I see it, I reach for medicated shampoo. I was told by my vet that it is yeast.
If that's what yours has, it's easy to get rid of by shampooing with Chlorexadine 4% (non-prescription, anti-bacterial shampoo). It's sold by vets, online or at specialty animal supply stores (not Petco/Petsmart AFAIK
). I just paid $10 for a bottle at a local supply store, and it's $30 from my vet. That shampoo has worked some near miracles in itchy, miserable shelter dogs.
The Chlorhex bath may need to be repeated in a week. It also needs to sit on the skin for a good 5-10 minutes (follow bottle directions). It's an easy thing to try, pretty low cost and it will either work or it won't -- if not, you can move on to allergies or other possibilities.
I would also consider adding some organic, unrefined coconut oil to the diet (it combats yeast and many other things from the inside). Just start out very small, as a sudden yeast die off could make him feel lousy ("herxing"). I personally start them with less than 1 TEAspoon total, and slowly work up to around 1 TEAspoon per 10#.