Andy Thanks so much for all your replies! That is the one I am referring to, I should have posted the paintings. The portrait of Robert Rogers was an interpretation, so it is unlikely the artist ever actually saw him. I almost wonder if the artist did not base the uniform in this portrait on the uniform of Johnson in The Death of General Wolfe, or if the man in the green jacket in that painting if actually meant to be Robert Rogers, as I have heard it posited. I assume one of the straps in the Rogers portrait is meant to be for the bag, and one is meant for the powder horn. I agree that the straps in the paintings are supposed to be beaded, however I will go with woven simply to be on the simpler side since the ranger company I am joining airs of the side of simpler. As for good old Major Rogers from Northwest Passage (which is a fantastic movie) the bag is much more plausible than the dyed green fringed buckskin outfits.
As far as what they are made of I would say TDoGW depicts a brown leather strap with wampum beads and red tassels, and it looks like the bag itself may have tassels or mesh on the front of it. I think the one in the portrait of Rogers is the same but the leather might be meant to be painted red.
If I was going to build this bag I would do a dark brown cow or elk leather bag, with red tassels on the flap, and I would either do a woven strap with the design woven into it, or a brown leather strap with a white thong laced through it and tassels on the edges made from the red embroidery floss. I would also make the strap adjustable, but with a thong laced through a series of holes rather than with a buckle. Let me know if you decide to build one, and I also want first refusal.