Flares can come in handy in low-light situations. If thrown or dropped, any targets standing in the vicinity of the flare are treated as if in daylight, making them a lot easier to hit with ranged attacks if darkness is causing a penalty to accuracy.
Although the flare will only normally inflict up to 1 damage when hitting an enemy, aiming at the eyes/head and scoring a Critical Hit can blind/knockout or even instantly kill (requires Better Criticals perk), regardless of their armor. When combined with Living Anatomy, flares will do at least 5 damage to any organic target since they only need one AP to throw. This will allow a character with an Agility of 10 to outperform many starting weapons in terms of damage dealt per turn.
In Fallout, they can also be sold for 35 bottle caps, which can be quite helpful early on for players who have little money.