The Webster 1913 entry for 'flannel' has obviously gone walkabout, scanned as Flannnel or something*, so here's what the Chambers dictionary says about it:
a soft woollen cloth of loose texture for undergarments, etc.: the garment itself
Flannel underwear has probably been around longer than fashionable flannel. It is the common material for pyjamas. In the plural, flannels are the white garb worn by cricketers, who are therefore sometimes called flannelled fools.
A flannel is also another name for a facewasher or facecloth.
Chambers gives two possible etymologies, Old French flaine 'blanket', or Welsh gwlanen from gwlan 'wool'. (An obsolete or dialectal form of the English word is flannen.)
As a verb, to flannel is literally to swaddle in, wrap in, or rub with flannel cloth; and figuratively to bamboozle, pull the wool over someone's eyes.
* Found it, June 2004: it was under Flanel.