Cotton and linen are really prone to damp, and throwing a nice soldered tin box in the fire is not a option
Cans are convenient but they're not necessary to make char cloth - just wrap it on a stick; get it to start to char, and then put it out real quick - I've rolled it against the bottom of my kettle or such to put it out, but just putting it out with your hand will work too - it's not all that hot, unless maybe you've got baby soft hands.... IIRC it was Karl Koster whoe mentioned making char in a similar way on another board.
Then again no reason you can't just make it in your kettle -- a bit large, but it will work in a pinch.
As to lack of mention for char "cloth" specifically - yep not much early on, but there is a fair amount of documentation that mentions just "char" or "tinder" with no further description. KK mentioned that too...
Cotton and linen are really prone to damp
Here in the high, dry Rockies that's not much of a problem (average humidity 20% or less most of the time) and charred anything tends to draw moisture in my experience......
The mountain men carried a little parfleche bag, maybe 3" by 5", often in front of a pipe bag. This little bag was called a strike-a-lite bag and held the flint and steel. As I said the flint and steel were not carried in a tinder box. There are a lot of late 1800's strike-a-lite bags but pre-1840 are few and far between. Jim Baker has one in the painting of him but the painting was post 1840. By the way some folks erroneously call a pipe bag a strike-a-lite bag. The pipe bag was much longer and larger.
Most strike-a-lights are made from a combo of a parfleche nack (rawhide for the pilgrims)and braintan front. There are a fair number of pre-1840 ones still extant made by the Kiowas. In the later reservation years these pouches while still called strike-a-lights, were in fact more often used as ration card cases.
There are a few, very few, of what we now call pipe bags from pre-1840. One was illustrated by Bodmer and is in a collection in Europe, but all the early ones are fairly short and sparsely decorated in comparison to the long, fancy ones which start showing up around the mid-1850's, but were not popular until about 10 years later.
In fact there is little written or other documentation of the mountaineers wearing a belt pouch of any kind. Osborne Russell does mention a tobacco pouch being worn on the belt, but exactly what it looked like is unknown. One of the few examples of a belt pouch used by a "white" is the one shown being worn by the interpreter (possibly Toussaint Charbonneau who was more than likely a metis) in Bodmer's painting of the Prince and Bodmer meeting Indians outside the fort. It is one of the pouches with an integral belt - you can see a couple of pouches of a different shape but still with this attached belt on the Splendid Heritage site.
as always others mileage will vary.....