Lost in a Harem (1944) on Netflix

Pete Johnson and Harvey D. Garvey, two inept magicians on tour in the Middle Eastern kingdom of Barabeeha, help disenfranchised young Prince Ramo regain his throne from his devious Uncle Nimativ, who uses two magical hypnotic rings and ruthless methods to maintain his power. By posing as Hollywood talent scouts the boys break out of a dank dungeon with a deranged derelict, evade palace guards, elude the palace executioner, and avoid detection in the forbidden royal harem.