Green’s Dictionary of Slang

flapdoodle n.1

[SE flap, something hanging down + doodle n.2 (1) although this predates]

1. the vagina.

[UK]Urquhart (trans.) Gargantua and Pantagruel (1927) I Bk I 44: Another [would call it] her sugar-plum, her kingo, her old rowley, her touch-trap, her flap dowdle.
[UK]Farmer & Henley Sl. and Its Analogues.

2. the penis.

[UK]Farmer & Henley Sl. and Its Analogues.

3. a sexually incompetent man, either one who is still too young to have had sex or one who is now too old to attempt it.

[US]Maledicta IV:2 (Winter) 190: Flap-doodle, doodle-flap, flapper and floater may refer to a young boy or to an old man, the one never having exprienced a cock-stand and the other a matter of memory.