1560s, "one who or that which flaps," agent noun from flap (v.).
A sense of "very young female prostitute" is recorded by 1889, but the word is used also in contemporary sources in the sense of "any young girl." The original suggestion seems to be the long braids or ponytails that were customary for younger girls to wear (opposed to the updos of adult women) which could themselves be called flappers or flaps.
When I first caught sight of the Flapper she was standing on the island in front of the Ritz […] I studied her thoughtfully, the blue serge coat and Peter Pan collar, the familiar sailor hat with the school ribbon round it — I started. Ye gods! Her hair! The customary long chestnut plait had disappeared. Had she in the course of some outrageous prank cut it off? Sacrilege! […] "Flapper!" I demanded sternly, "where is the Flap?" [...] It seemed that the Flapper had been allowed — “just for to-day, because it’s so near the end of the holidays” — to do her hair in a door-knocker instead of a plait. [A.E. James, “Trouble with the Flapper” The London Magazine, January 1911]
The fashion flapper began about 1895, originally indicating an outgoing, slim-figured adult woman who wore her hair in girlish braids, curls or ponytails. Early adopters tended to be athletes and professional dancers. It was associated with the area of Piccadilly in London and with the Gaiety Theatre formerly located on the Strand; but by 1914, an article in Vanity Fair was jokingly lamenting "the passing of the Flapper" in favor of new feminine styles. Yet the term remained in use for young girls generally, and soon was applied ("flapper-length skirt") to the new fashion for short skirts (similar to what young girls traditionally wore instead of the ankle-length skirts worn by adult women) by 1916.
Because the old flappers of Piccadilly were often chorus girls, the term extended to actresses by 1912 and by 1917 it had come to designate a working woman of any profession. In Britain the word took on political tones in reference 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]
The sense of "sexually licentious woman" is by 1914, probably derived from the chorus girl/actress sense rather than the young prostitute sense (the chorus girls had a reputation for living off the financial gifts of male admirers). This is the sense most often felt in 1920s texts decrying the flapper.
Immodest Dress. - For some strange reason too many of our modern girls seem to enjoy being called flappers. She glories in the lustful looks and vulgar comments which her appearance calls forth on the street. With bobbed hair, three coats of paint and powder, with plucked eyebrows, artificial eyelashes, and carmine lips, with low necked, short sleeved, and generously peekabooed waist, with an abbreviated skirt and rolled down silk hose, just meeting below the knees, and all the rest of it, she blithely pursues her ill fated course. If people turn to stare in horror stricken amazement, her costume is a success; if she passes unnoticed then something must be done. Her sketchy costume cannot fail to arouse the passions of men and boys. To all outward appearances she is attempting to imitate the woman of the streets. And she succeeds. [J.L. Nichols, "Safe Counsel; or, Practical Eugenics" 1927]
It may be worth noting that the above description comes from a science textbook.
