Not exactly.....from Wikipedia...
Barry Popik of the American Dialect Society found an example from 1940, as well as this from the sports section of the
San Francisco Examiner of 8 February 1942: “Answer these questions correctly and your name is Flynn, meaning you’re in, provided you have two left feet and the written consent of your parents”. To judge from a newspaper reference he turned up from early 1943, the phrase could by then also be shortened to I'm Flynn, meaning “I’m in”.
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In later years, the rhyming phrase became associated with actor
Errol Flynn, who had a reputation for womanizing, consumption of alcohol, and brawling.