I thought of that too, of course, but it turns out to be from powder 1 ("A substance composed of fine dry particles") instead. Sense 5a is “A medical substance formulated as a powder, originally for external application, later also for internal use (usually taken with liquid); a measured dose of this, esp. when pre-packaged (frequently in plural),” from which develops P3 ”colloquial (orig. and chiefly U.S.). to take a (run-out, walk-out, etc.) powder: to withdraw; to depart, absent oneself; to run away, abscond. Recorded earliest in to take a run-out powder at run-out adj.2.” The first few citations:
1909 San Francisco Chron. 4 Feb. 9/2 Senator Cockey O’Brien of Bernal Heights..made Senator McGluke take a run-out powder.
1934 J. Proskauer Suckers All xxiv. 279 The smartest guy in the office took a walk out powder this morning.
1940 J. O’Hara Pal Joey 72 And take a powder out of here that day.
1941 R. Chandler in Street & Smith’s Detective Story Mag. Sept. 25 Why are you taking a powder?