In Grant's book on the hunting pouch, there are one hundred original pouches shown with their powder horns attached. Of these, only eighteen horns were hanging below the pouch flap. The flaps on almost all of these bags were buttoned. All of the rest, 82 of them, had the horns hanging in such a manner as to hold the flap down.
In this same book, and in his book on powder horns, of the ones that have their original straps, they are all very thin with one exception.
As far as positioning, the only photos of people wearing bags and horns, it appears that most carried the bags a little bit to the front of them instead of directly under the arm on the side. One photo of Joe Young shows him with his horn strung around his neck so as to hang in front of him to the right, and the strap doesn't even go around behind him; it's just hung around his neck.
There is one painting that looks like an English officer; the strap on this bag and horn looks to be four to six inches wide and very decorative. So as far as historical correctness, it seems that most of the time, the horn should be mounted off of the bag strap in such a manner as to help secure the flap.