The Firefly Burner is a rare ARC component added to Arc Raiders in the Shrouded Sky update (patch 1.17.0). You need it to complete the final stage of the Weather Monitor System project, and the only way to get one is by destroying a Firefly — one of two new flying ARC enemies introduced alongside the Comet.
Quick answer: Kill a Firefly drone and loot its corpse. The Firefly Burner drops consistently with nearly every kill, so you typically only need to take down one.

What the Firefly Burner is used for
The Firefly Burner is classified as a rare, recyclable material with a weight of 0.75 and a sell value of 1,000 coins. Its primary purpose is completing the Weather Monitor System project, but it also serves as a crafting ingredient. Combined with one Synthesized Fuel and two Crude Explosives at an Explosives Station 3 (plus the Trailblazer Blueprint), it produces a Trailblazer. If you don't need it for crafting or the project, recycling a Firefly Burner yields two ARC Alloy and two Crude Explosives. Salvaging returns two Crude Explosives.

How to identify a Firefly
Fireflies are flying ARC drones that look similar to Hornets at first glance, but a few visual details set them apart. They have a pointier, jet-fighter-like silhouette and an extra metal plate on top that almost looks like a small hat. More critically, all four of a Firefly's rotors are armored from every angle — Hornets only armor two rotors, and only from the front. If you're ever unsure, you can tag the enemy to confirm its type.
The biggest behavioral difference is the weapon. Instead of a taser, the Firefly carries a flamethrower. It closes distance aggressively and sprays fire at short range, making it far more dangerous up close than a Hornet. Getting caught in the flames while a nearby Hornet stuns you is often fatal, since the burn damage ticks through the stun duration and you can't run.

Where Fireflies spawn
Fireflies patrol outdoor areas on every map in Arc Raiders. They join Hornets and Wasps in their standard patrol routes and crash down from orbit the same way those enemies do. They appear during both regular raids and hurricane map conditions, though there's no confirmed evidence that hurricanes increase their spawn rate.
Dam Battlegrounds is a particularly reliable farming spot. The area around the Hydroponic Dome Complex and the swamp has always been dense with flying ARC enemies, and Fireflies now mix into those spawns. The Spaceport, Buried City, and Blue Gate are also solid choices. Fireflies can even show up on Stella Montis in the more open interior areas like the Loading Bay or Lobby, though outdoor maps offer more frequent encounters.
Best weapons and tactics for killing Fireflies
The core combat loop mirrors fighting a Hornet. You want to destroy the rotor fans — either shoot the two rear rotors directly or strip the armor off the front two and then take those out. The difference is that Fireflies are tougher due to their all-around armor plating, and they punish hesitation with devastating fire damage.
Heavy weapons are the most straightforward solution. A Ferro gets the job done, but an Anvil is better for the faster time-to-kill. If you have access to a Hullcracker, it can two-shot a Firefly, which essentially removes the danger window entirely.

Seeker Grenades are an excellent budget option. They home in on flying targets and deal heavy damage, making them one of the most efficient tools against any airborne ARC. Wolfpack grenades (homing) work well too.

If you lack heavy weapons or good grenades, the Firefly's yellow gas canister is a critical weak spot. Landing shots on it can bring the drone down in as few as two hits with a precision weapon. Missing the weak spot, however, means dumping an entire magazine into thick armor while the Firefly closes in and sets you on fire.
Looting the Firefly Burner
Once the Firefly crashes, walk up to its wreckage and loot the corpse. Unlike the Comet Igniter (which requires you to loot a specific central core piece before the enemy explodes), the Firefly Burner drops straightforwardly from the destroyed drone with a high consistency rate. There are no separate parts to worry about — just loot and go.
Remember that you still need to extract successfully to keep the Firefly Burner. Dying with it in your inventory means losing it, so play cautiously after picking one up if you're on a dangerous map or low on healing.

The Firefly Burner is one of the easier new materials to farm in the Shrouded Sky update, especially compared to the Comet Igniter's tighter kill window. Bring a heavy weapon or a handful of Seeker Grenades, head to any outdoor-heavy map, and you should have one within a raid or two.