As has been mentioned by a couple of fellow Pemberleyans below, a waistcoat was worn over a gentleman's shirt and flannel was a woolen broadcloth. I would like to add that Marianne disliked the Colonel's waistcoat because it was practical and unfashionable. A fashionable young gentleman would not have worn a waistcoat made of something so plain and functional as wool, but would have gone for a more stylish look-- Marseilles quilted fabric, silk brocade or perhaps a nice white piqué. A young gentleman might wear a waistcoat made of striped toilinette, which is a material with a silk or cotton warp and a wool weft, but it was a very fine wool and those modish stripes would have set it apart from the dull-&-boring-but-warm flannel that the Colonel was wearing.

There were also such things as under waistcoats and slip waistcoats. An under waistcoat could be of flannel and was worn for warmth beneath a waistcoat of a more fashionable fabric. Col. B. may have worn a flannel waistcoat without anything fancier over it, though. Slip waistcoats were of lighter weight fabrics and one, two, or three would be worn underneath a waistcoat of heavier cloth. These slip waistcoats could be of different colours and patterns; they need not match.