Green’s Dictionary of Slang

(US Und.) to escape, to disappear.

1922		Appleton Post-Crescent (WI) 6 May 11/1: Flapper Dictionary houdini – To be on time for a date.
1933		Ersine Und. and Prison Sl.
1935		A.J. Pollock Und. Speaks n.p.: Houdini, to disappear.
1980		G. Liddy Will 114: As if in fear that Leary would Houdini out of his pants again at the first opportunity, the district attorney ordered me to interview him immediately.