"i'd be curious what this fabric store stuff is..."
I think what you are talking about is Cotton Batting. Cotton batting is the matt of cotton fiber that you use as the "stuffing" in a quilt. Please excuse my ignorance of sewing terms, but Batting is the stuff that is used for "stuffing". Sort of like a loose cotton felt.
I have never tried it as tinder, but now that you mention it, it probably would work. You will also find polyester batting and poly blends that would probably not work.