The word comes from the game of Musolum, a game in which players say a made-up word in an attempt to catch others off guard. If the recipient of the made-up word responds with any word such as huh?, wha?, hmm? or whadjoosay?, the recipient is then flumhummed.
Note: Flumhumming is not the same as musolumming. Musolumming is initiated by an intentionally misspoken word, whereas flumhumming can happen with no provocation or forewarning.