Restart the Engines
To restart the engines in Chapter 3: Course Correction, Isaac Clarke must refuel both the North and South engines and then reactivate the Centrifuge. Begin by navigating to the Refueling Control Station to refuel the North engine, using Kinesis to pull down the mechanism. Repeat this process for the South engine on Floor 4.
After both engines are refueled, proceed to the Centrifuge on Floor 2. Inside the Centrifuge, attach the two generator modules using Stasis and Kinesis. Once the Centrifuge is restarted, Isaac will need to escape back to the Control Room without life support while the Centrifuge rotates at maximum velocity. Take the Cargo Lift down and run clockwise around the Centrifuge, using safe points for shelter. Stasis will not slow down the Centrifuge.
Later, in Chapter 10: End of Days, Isaac will need to test fire the engines after installing the Singularity Core on the Executive Shuttle. During this process, the Hunter will appear. Down the Hunter behind the engines, use Stasis on it, then quickly return to the Shuttle Control to "test fire the engines" with the Hunter directly behind them.
The Flamethrower weapon can be found in the corridor leading to Fuel Storage, just before reigniting the engines. This area will be heavily corrupted. The weapon is held by a corpse being consumed by the Corruption in the wall.