The Flute of the Outer Gods says the following (emphasis mine):
Any Phase: Lose 3 Sanity and 3 Stamina and discard Flute of the Outer Gods before making a Combat check to defeat all monsters in your current area. This does not affect Ancient Ones.
Another answer on this site about the Flute states that it can be used at either a location or a street. However, there are other locations that monsters can be, such as the Outskirts and The Sky, but you can't attack those so it's moot about whether you can be used there.
But what about monsters that are in a location where you can attack them, but are not "on the board"? For instance, there is The Terrible Experiment rumor that says the following (emphasis mine):
When this card enters play, place 5 monsters from the cup on it. Any player may choose to fight one or more of these monsters while in the Miskatonic U. streets during the Arkham Encounter Phase. If defeated, they are claimed as monster trophies. These monsters do not move, are not considered on the board, and do not count against the monster limit.
Are they in "your current area" despite not being on the board? Can you attack one of these monsters, pass a Horror check, then instead of a Combat check use the Flute of the Outer Gods to destroy all of the monsters? This came up in our last game and we weren't sure how to resolve it.