I use leather I had left over from an old Tandy kit and some other small pieces of leather I picked up somewhere just because I thought I might have a use for it someday.
If you have a thin old leather belt around, that might be a good source of leather for a flint wrap.
It doesn't have to be big. Just enough to cover the upper and lower jaw and wrap around the end of the flint by somewhere around the same width as the jaws on the ****. You could just "shorten" the belt by cutting off about 1 1/2 inches from the end that goes thru the buckle first.
If you are at all talented you can then trim the end back to the shape it used to be before you cut if off and no one looking at the belt will know the difference.
You are looking for some fairly thin leather. Maybe about 1/16 to 3/32 thick.
Leather much thinner or thicker than that doesn't seem to work as well for me.