Green’s Dictionary of Slang

1. having a large mouth.

1881

‘Bill Nye’ Bill Nye and Boomerang 155: The [...] lantern-jawed, sway-backed, mangy, flannel-mouthed poet of the educated and refined East.

2. (also flannel-mouth) loud-mouthed.

1881		Oskaloosa Herald 17 Mar. in Miller & Snell Why the West was Wild 311: The mayor is a flannel mouthed Irishman and keeps a saloon and gambling house.
1901		Intermountain Catholic (Salt Lake City) 5 Oct. 4/3: The same stupid vulgarities concerning [...] flannel-mouthed Irish and chicken-stealing niggers.
1905		F. Hutchison Philosophy of Johnny the Gent 79: ‘ He's a big flannel mouth rummy that's been readin’ some o' them Hawkshaw the Sleuth tales’.
1933		Ersine Und. and Prison Sl.
1939		N. Algren ‘Lightless Room’ in Entrapment (2009) 44: He yelled over to me I was just one more flannel-mouth Polack.
1940		E. O’Neill Long Day’s Journey into Night II ii: That flannel-mouth, gold-brick merchant.
1942		N. Algren Never Come Morning (1988) 44: He’d get them all in trouble some day with that flannel-tongued trap of his.

3. (Can./US) well-spoken.

c.1930		(ref. to mid-19C) N. Kimball Amer. Madam (1981) 23: The family was always hard and fast church goers, always with its ass out of its jeans, flannel-mouthed and proper.
1950		R. Starnes And When She Was Bad 75: I have seen the same dodge worked to death by other policemen and by many a flannel-mouthed lawyer.

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

1931

E. Hemingway letter 1/12 Nov. in Baker Sel. Letters (1981) 344: This damned typer skips like a stammering flannel mouth nigger.