I made one of those twined bags, a bit simpler than TOF's, last year. I like it but...
As far as I can tell, twined gun bags don't seem to have been used historically, and by the 18th century the use of twined bags in general - for food storage and such - was mostly limited to the Great lakes area, at least east of the Mississippi. I'd love to be able to say otherwise, but after a lot of searching through museum catalogs, art books, etc., twined bags suitable for carrying gun stuff in and dating to the historic period are conspicuous by their absence. My conclusion is that they are probably a fantasy item, like hilted "rifleman's knives" and Woodbury school iron-mounted rifles. Which is a pity, 'cause I like mine, despite the problems with the dye I used....
Incidentally, I've never seen an 18th century Cherokee pouch, or really much of 18th century anything apart from a tomahawk and a strap. Really hard to find anything from the SE from that period. Quillwork is a northern thing, too, unless the they were trading for quills - no porcupines down here.
I'm not sure what period you are shooting for, but by 1775 the Five Civilized Tribes had hunted the deer in their territories out and were moving from an economy based on subsistence farming and market hunting to a more European-style agricultural system, complete a heavy dependence on African slaves (Gardening was women's work and below the dignity of an Indian male, but they needed more manpower...) with a heavy emphasis on raising cattle and horses (working with animals, on the other hand, was proper manly work). They were also living log cabins, and dressing very similarly to the White frontiersmen, I believe - I think that the big difference was that the Whites wore hats, whereas the Indians went bareheaded. I dunno if they were making bark-tanned leather at that time, but I do recall reading about raiders stealing hides out of tanning vats in Kentucky, so they liked the product even if they weren't making it themselves at that time.
In other words, by that period there would probably be very little in design, material, or decoration to distinguish a SE Native set of accouterments. Regardless of who produced it, a plain 'ole pouch of bark-tanned leather, or possibly coarse cloth, would be the most likely companion to a c. 1775 smoothbore down here....
