Green’s Dictionary of Slang

flannel-mouthed adj.

also flannel-tongued
[predates flannel n.2 ; note SAmE flannelmouth, a very large catfish]
(orig. US)

1. [late 19C] having a large mouth.

2. [late 19C+] (also flannel-mouth) loud-mouthed.

3. [20C+] (Can./US) well-spoken.

4. [1930s] talking thickly or with a brogue [the idea of talking with a SE flannel in one’s mouth].