Green’s Dictionary of Slang

(US) a person with a notably large mouth.

1655		Gossips Braule 6: Yes, yes, Mistris Flownder-mouth, you shall have thanks with a Pox to ye, ye old Lecherous Jade you.
c.1770		‘To Mistress Mouse’ in Buck’s Delight 8: With a flounder mouth and snotty nose.
1772		Bridges Burlesque Homer (3rd edn) 161: He falls, and sprawls about in blood, / And fills his flounder-mouth with mud.
1968		in DARE.