As you can see, we have a mini-Schnauzer, Phoebe Buffey, about 4 years old . She's had a scratching behind the ears habit for a few years, not real bad, just a little irritating (to me). I think it's just that, a habit. But I don't know much about dogs. It hasn't affected her hair or skin, that I can tell. Our vet provided us with some expensive shampoo & cream rinse. Virbac animal health dermatology Pyroben & Epi-soothe. I alternate between that and some Premium brand natural oatmeal shampoo I got at Walmart. I haven't really been able to tell that it makes any difference.
I just looked at the ingredients of the prescription cream rinse and it also has collodial oatmeal in it. I personally think it's a little ridiculous to worry about the miniscule amount of gluten that could possibly be in the oatmeal shampoo (which you rinse out anyway) from potential cross-contamination, which would then have to be ingested by me. I mean, I would have to lick my dogs hair a lot. But then, I think a lot of things are ridiculous, there may be something wrong with me

. Now if you have DH that might be a different story. I don't have DH and none of the other posters have said if they do.
Or, If you had an unexplained glutening problem and were searching for any possibilities.
best regards, lm