I don’t know if it would specifically help with allergies, but we just started using head and shoulders for ours because he was getting a little bit of flakes. I would never have guessed it was safe for dogs but apparently tons of groomers use it.
In studies, I don't think any type of special shampoo has shown effectiveness for reducing pet dander. I believe that weekly bathing provides the best benefit.
Just make sure that you (and the dog) aren't allergic to any of the shampoo ingredients. We can't use lots of different shampoo brands on the cats because I'm allergic to the scents.