My GSD bitch has that black skin diseases (I can't remember the proper medical term) and all has to do with her thyroid. I manage this with Oroxine (thyroid meds) and Macrolone. When the seasons change I sometimes have to adjust the dosage and one of the symptoms of needing to change the dosage is a lot of scratching, licking and dry flakey skin. The flakey skin looks just like dandruff when I brush her.
Just something to keep in mind if she doesn't improve, otherwise I wonder if it is the shampoo you used or maybe you didn't rinse it all out. My 2 only get a bath with shampoo once a year, otherwise bathing them too often strips their natural oils from their coats.