1540s, "to dash, plunge, flop," perhaps from Scandinavian (cf. dialectal Swed. flunsa "to plunge," Norw. flunsa "to hurry," but first record of these is 200 years later than the English word), said to be of imitative origin. Spelling likely influenced by bounce. Sense of "anger, impatience" began to adhere to the word 18c. Related: Flounced; flouncing. As a noun, from 1580s.
"wide ruffle," 1713, from M.E. frounce "pleat, wrinkle, fold" (late 14c.), from O.Fr. fronce "fold, gather, wrinkle," from Frankish *hrunkja "wrinkle," of unknown origin. Influenced in form by flounce (v.).