As a lover of natural fibres and all their glory (thankyou for that, Medieval Re-enactment), I am no stranger to The Burn Test.
Briefly, for those uninitiated, this is where you're not sure of a material's natural or man-made properties, so you take a small sliver of it and apply a flame. Natural fibres burn and create ash, man-made melt and leave puddles and/or beads of crud.
Griffin Dye Works has a nifty little guide to Burn Test results, to help you figure out things a step further than "natural" vs "man-made", which includes an all too important "poisonous fumes" box! Nifty.