Green’s Dictionary of Slang

to fall or throw oneself down suddenly; to throw down.

1852		H.B. Stowe Uncle Tom’s Cabin 58: Flap down your fifty, If we get the job, and it pays, I’ll hand it back.
1905		Bulletin (Sydney) 21 Sept. 40/1: [B]ut ballroom style is too sudden. Yer ’ave ter get round like a monkey wid a package o’ live crackers on ’is tail – yer no sooner up this end o’ the room than yer down that, ’n’ ten ter one if yer don’t finish up by chuckin’ a flap an’ landin’ with a ’eavy bundle o’ drapery on yer chest.