I checked my copy of Madison Grant's "The Kentucky Rifle Hunting Pouch" and he barely mentions lined bags. Bags with lined flaps that had piercings to show the tradecloth or color dyed leather beneath were briefly popular around 1820 and, he estimates, the introduction of the sewing machine made other style of ornamentation possible. (see page 45). Other than that, I couldn't find mention of linings from him. Unfortunately, of the dozens of pictures, none have the flap up so you can see ant possible linings.
If you're interested in buying one, I would ask the craftsman for his source of authenticity (some have studied originals). If you are making your own, I would shy away from a lining.
I have two I made with red wool cloth under the flap and a deerskin piece sewn underhneath to sandwich it (one I used rubber cement to hold the wool to the deerskin. The wool was left about 1/2" larger than the outer flap and I "pinked" it to form a jagged edge. It looks official. My source was a Tandy Leather Co. pattern book (hey, what did I know?). I have since seen other modern bags that have the same design elements, and I wonder if the original is out there or if others have used that same pattern book. :hmm: