The story
Likely from flossy “resembling floss”, thus “showy” or “soft”. Compare floozie. Possibly from Flossie, diminutive of Florence or Flora. Attested from the beginning of the 20th century.
Etymology from Wiktionary, CC BY-SA 4.0.
flossie
Today it means: A sexually promiscuous person (usually a woman); a sex worker, prostitute. Full definition →