As has already been stated, you can use any natural fiber clothe. The synthetics usually melt. And WELL WASHED. New material often has chemical sizing (and sometimes flame retardant) on it. So the more washed/used the clothe, the better it will work. That washing tends to expand and ... fuzz up ... the individual fibers in the fabric. All that finer fluffier texture in your charclothe helps catch a spark better.
Historically, written documentation for charclothe has not been found before the time of the American Civil War - 1860's. So it's use before then just isn't documented. Before that time, the most common way to catch a spark was with charred punky wood - like old coals from your last fire. But they also wrote about using Tinder Fungus (innonotus obliquus) directly off of the Birch tree without any other preparation, or slices of shelf mushrooms charred just like you do when making charclothe, and amadou (a shelf fungus layer soaked in potassium nitrate). Yes, they did know about charred clothe catching sparks before the 1860's, but it just hasn't shown up in any written form or artifacts before then. They knew about matchcord for a matchlock gun well back into the 1600's and before. They also knew and used tinder tubes in the early 1800's. But just didn't write down anything about charclothe earlier. And nobody has found any properly documented examples from earlier times. Plus no "tin" for making charclothe has been found either.
Just some of those ... pesky little details ... lost to history.
Mikey - that grumpy ol' German blacksmith out in the Hinterlands
