"forward young woman," 1921 slang, from
flap (v.), but the exact connection is disputed. Perhaps from
flapper "young wild-duck or partridge" (1747), with ref. to flapping wings while learning to fly; but other suggested sources are late 19c. northern Eng. dialectal use for "teen-age girl" (on notion of one with the hair not yet put up), or an earlier meaning "prostitute" (1889), which is perhaps from dial.
flap "young woman of loose character" (1613). In Britain the word took on political tones in ref. to the debate over voting rights.
" 'Flapper' is the popular press catch-word for an adult woman worker, aged twenty-one to thirty, when it is a question of giving her the vote under the same conditions as men of the same age." ["Punch," Nov. 30, 1927]
[flap-er] 
ər