But they have never shown up. Does anyone know why?
The point is to sell it or drop it to the ground.
I've never had them not turn up...but it probably does have something to do with how many settlements you have, and how well developed they are.
As others have said, I'm guessing it involves range. If you're at the southern part of the map and all of your settlements are to the far north of the map, it's not realistic to expect them to be there right away. It's not realistic to expect them to see the flare in the first place, but I'll suspend that disbelief.
However, if your traveling in the south and you have settlements established at Somerville Place, Jamaica Plain, etc. it's more realistic to expect them to show up quickly. It's not an instantaneous appearance though. If you're in the middle of fighting a legendary deathclaw and want to call for backup, they're probably not going to make it there quickly enough.
Do you have the artillery set up in all of those settlements? Are all of the artilleries manned? If so, I don't see why it wouldn't work
I'm guessing that the turning point on the flare gun is when you start to encounter Minutemen as you wander about. (Where do these guys come from? I have Preston as my constant Companion, and while settlements have allied with us, we've NEVER inducted anyone into our ranks as full-time Minutemen. I swear, the Minutemen that I encounter I have NEVER seen before.) Anyway, once the free-roaming full-time Minutemen are active, I'm guessing they become available to be summoned by your flare.