Green’s Dictionary of Slang

flush v.1

[some punitive whipping was still carried out in public; the horse is a wooden frame to which the victim is secured]

to whip; thus flushed on the horse, privately whipped in prison.

[UK]Hotten Sl. Dict. 136: FLUSH, to whip; ‘flushed on the horse,’ to be privately whipped in jail.
[UK]Sl. Dict.