How does Flute of the Outer Gods work in Arkham Horror and when should I use/buy it?
The card specifies area because it could be either a location or a street. I'm pretty sure they already had the 'neighborhood' terminology worked out when the base set came out and they didn't use it here for a reason. The flute's use is basically 'Instead of rolling a combat check against a monster when you normally would, you can use the flute instead.' So you need to survive the monster's horror check before you can use the flute. If you don't survive the horror check, you don't make it to the combat phase, so you can't use the Flute.

Note that as the flute kills everything in the location/stree that you use it in, you can enter combat with a weak monster(Cultist, horror check auto-success), use the Flute, and kill everything in that space, which happens to be a Gug/Dhole/Color/Servitor/Mask/etc.

So with a regular gate opening, the flute doesn't give as much bang as it could, as there's usually only 1-2 monsters in a location. But after a monster surge or two and there a location full of monsters that just happen to all move on the same symbol, the flute becomes a great way to take out a horde that would've dealt that damage to someone anyway.

Granted, the Flute is also useful if you just happen to not have the resources available to take out something with good odds, as you strictly only need enough sanity to survive failing the horror check to use it. You don't even need the 3 stamina 3 sanity to use it you know! As the Flute does damage and isn't a cost, you could use it at 1/1! You'd be devoured of course, but that's the cost...

In my gaming group, it's pretty rare that someone will choose to buy the Flute over something reusable when they go shopping, but if it happens to be gotten for free, no one complains.