This video shows what happens when hang up a cotton quilt and light it at the bottom. You can buy quilts just like this from my molecule quilt shop! home.theodoregray.com/moleculequilts (this one is a slightly incorrect version of estradiol, in other words it's a girl-baby quilt).
This is the absolutely worst-case scenario for demonstrating flammability. There is an ample supply of air from both sides, and the fire can work its way uphill all the way, as fire likes to do. Placed on a flat surface, or rolled up, the quilt would burn much more slowly.
This quilt was made with 100% cotton fabric on both sides and 80% cotton, 20% polyester batting. Under more normal conditions it will (obviously) sustain combustion, but is fairly easy to stomp or swat out.