"Flap jaw" is a slang term used to describe someone who talks excessively or doesn't stop talking. Antonyms for "flap jaw" would be terms that describe someone who is not talkative, has little to say, or is reserved. Some possible antonyms include quiet, concise, reserved, succinct, laconic, discreet, and taciturn. A person who is not a "flap jaw" may be regarded as someone who is more thoughtful, introspective, or introverted. Depending on the context, the opposite of a "flap jaw" could be seen as someone who is more respectful, listens carefully, or is willing to take the time needed to think things through before speaking.