(noun)
a garment or other textile made from flannel fabric, such as long underwear (used in cold weather), men's outerwear (such as trousers or button-down shirts), or a washcloth;
e.g. She used a small flannel to wash and dry her face before going to bed.
(noun)
in informal British usage, bland talk that may be flattering or evasive, usually used when trying to avoid talking directly about a difficult situation or subject;
e.g. He prefaced his request with a great deal of flannel because he was shy.
(verb)
in informal British usage, to use flattering, evasive, or bland talk in order to avoid talking directly about a difficult situation or subject;
e.g. She chose to flannel on for a bit before bringing up the issue she wanted to discuss.