Green’s Dictionary of Slang

flutter n.2

1. any form of sexual experience; thus be on the flutter, to be a sexual sophisticate; do/have a flutter, to enjoy hedonistic rather than procreative intercourse; have had a flutter, to have lost one’s virginity.

[UK]Farmer & Henley Sl. and Its Analogues III 40/2: To have had a flutter [...] = (1) to have been there [...] (2) to have lost one’s maidenhead.
[Aus]X. Herbert Capricornia (1939) 88: If there are any kids as the result of these quite natural flutters they are just ignored.

2. (US, also flutterer) a male homosexual.

[[UK]J. Gay Distress’d Wife II viii: lady willit.: (Reads) A Dangler. One that passes his time Time with the Ladies; who says nothing, does nothing, means nothing, and whom nothing is meant. It puts one in mind of Mr. Flutter.].
[US]Monteleone Criminal Sl. (rev. edn).
[US] (ref. to 1930s–40s) Guild Dict. Homosexual Terms 16: flutterer (n., obs.): An effeminate male homosexual; a short-lived word invented by the press in the late 1930’s or early 1940’s.
[US]B. Rodgers Queens’ Vernacular 73: stereotype effeminate homosexual [...] flutterer.

In phrases

do a flutter (v.) (also have a flutter)

to have sexual intercourse.

[UK]Partridge DSUE (1984) 412/1: since ca. 1875.