I've been caught out before with a beautiful piece of fabric I bought off the internet from a private seller who told me it was cotton. After receiving it a burn test revealed it was rayon - highly flammable and totally unsuitable for children's clothes.
I've been meaning to share this - such tests/charts are widely available on the internet, but maybe you didn't know it existed?
Fabrics that are pure (e.g. 100% whatever) are much easier to determine. I have just done a burn test this morning on a fabric (the wool blend I mentioned) and it took four matches and examinations to figure it out. It's just a matter of studying how the fabric ignites, the quality and colour of the flame , the odour, and the resulting quality of ash or cinder it produces.
How to test your fabric:
Cut off a piece of fabric approx 1" x 2-3". Holding with a pair of tweezers (or a steady hand) light the fabric over a non-flammable source (e.g. outside on the concrete/driveway, grass) in a well-ventilated area.
Click on chart for larger version
And this nifty and succinct sum-up from here
• Ignites and burns quickly, may flare, leaves a glowing ember after flame is extinguished. Smoke is white or light colored and smells like burnt paper or leaves. Ash is light gray or white and very soft.
Protein (Silk/Wool, Cashmere, Alpaca etc):
• Burns slowly and shrinks or curls away from the flame. Will not stay lit after flame is removed. Very little smoke is produced but it smells like burnt hair (wool) or feathers (silk). Ash is a gritty powder or a dark brittle, easily crushable bead.
• Ignites and burns quickly and can continue to burn after a flame is removed—exercise caution. Fiber may shrink from the flame, melt, and can drip (DANGER) leaving a hard plastic-like bead. Burning these fabrics will produce black smoke and hazardous fumes. Nylon smells like plastic when burnt but can also can produce a celery-like smell; Acrylics burn with a strong, acrid, chemical smell. Polyester smells slightly sweet, also with a chemical odor.