At the moment they will grab lit flares and try to eat them, but spit them out without being harmed like any other physics prop. As the title implies, I think that trying to bite a lit flare should set the barnacle on fire and kill it.
There are not a lot of places in the vanilla game where barnacles and flares can interact, but it is entirely possible in Office Complex and of course map modders can put together two mechanics commonly found in the earlygame however they please.
I think if this worked flares would actually be a fairly valid tactic for killing barnacles because in the early game before the player has accumulated a lot of firepower barnacles are kind of time- and ammo-consuming to kill and if a bunch of barnacles are in a tight grouping a single lit flare could potentially kill more than one with a single use as one barnacle spat it out and it was picked up by another, rinse, repeat.