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 normally only inflict 1 damage if thrown at an enemy, aiming throws at the eyes of enemies can blind or even kill them instantaneously, even if they are wearing power armor. When combined with having Living Anatomy, flares become stunningly efficient throwing weapons, as each flare 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 a low money count.