There is some limited evidence that horns were attached to bags as early as the mid-18th century - there is a French illustration from the mid-1750s showing a Cherokee with what could be interpreted as a horn-bag ensemble. Also, Wallace Gusler wrote in one of his articles in Muzzleblasts that there were a couple of probate inventories from before the Revolution that listed a rifle and all its associated paraphernalia
except the horn, and he suggests that that could be because the horn was attached to the pouch and thus only listed as "bag." OTOH, there are horns with surviving separate straps dating from all over the place, and lots of bags surviving that don't have a attached horn.
So, as far as I can tell either way is probably correct, or at least justifiable, for any place along the longrifle chronology.
As for material, while originals are scarce, I think that leather, homespun linen/hemp webbing, and fingerwoven wool are attested either from surviving pieces or in original sources (Doddridge recounts weaving straps as a boy c. 1780 or so). For your late flint Eastern rifle I'd go with either leather or a plain hemp/linen strap. I use 1" hemp webbing from Turkeyfoot Traders, and it is about as simple and functional as one could wish for.
You really ought to get a copy of Madison Grant's
The Kentucky Rifle Hunting Pouch - it isn't a perfect resource by any means, but there is very little written about the subject and it is a good starting point. Also these articles:
http://ehcnc.org/decorative-arts/historic-trades/
