According to Hollywood When Silents Were Golden:

…some years after the movie was released, Houdini used the final sequence [AKA “Desperate Chances”] in a vaudeville act. One night Tommy [aka David Thompson] took his wife to see the act and found that after running the clip in which the stunt man faltered and the planes locked, Houdini referred to this as his narrowest escape. He then invited members of the audience on stage.  Wondering what Houdini’s reaction to him would be, Tommy joined the group.  The great escapist recognized him at once and, without the flicker of a lash, identified him to the audience as “the hero who saved my life in The Grim Game.”

Of course it was really Christopher V. Pickup in the upper plane who saved Robert E. Kennedy (Houdini’s stunt double) as he hung from the rope. Tommy actually flew the lower plane.

It appears Houdini first used it as part of his act at the Keith’s Theatre in Boston MA:

Harry Houdini, a mystifier, has returned to the B.F. Keith circuit after an absence of two years in pictures. Houdini , who is a favorite headliner, has selected the water torture cell mystery for his act. He is heavily manacled and in full view of the audience placed upside down in a huge bottle like receptacle filled with water, from which he must escape quickly or drown. Previous to this act a picture showing Houdini’s miraculous escape from death in their remarkable act at the Palace picture, “The Grim Game”.

[Indiana Daily Times December 24, 1921]

Another example of Houdini using it as part of his act was at Columbia Theatre [Orpheum Circuit] in Davenport IA:

Refurbished, redecorated and claimed a stop higher in the standing of its programs offered a much improved class of entertainment. With Houdini as headliner and Flo Lewis as supporting feature, the bill had variety, balance and plenty of intrinsic interest. Houdini “goaled” the local audiences with his tricks…He carries with him a piece of film from “The Grim Game” the motion picture showing a real collision between two airplanes 4,400 feet from the ground. He shows audiences the Hindu needle trick in which he fills his mouth with four packages of needles and a handful of silk thread. Upon pulling the string out, the, needles are all threaded. He concludes with the Chinese water torture cell…

[Daily Times August 27, 1923]

And thanks to a John Cox post, we know that he showed it [March 4, 1924] at the Jefferson Theater in Charlottesville, Virginia as part of his Spiritualism Lecture Tour:

• Houdini chases spooks in Charlottesville