Green’s Dictionary of Slang

(Aus.) a powder compact.

1940		J.R. Warren Murder in the Blackout 164: There was the girl’s flapjack inside.
1982		N. Keesing Lily on the Dustbin 35: First she may apply ‘spackle-filler’ (foundation make-up), then ‘lippie’ and powder from her ‘flapjack’ (powder compact).