After choosing D-Team's Fire fragment, you must escape the trash disposal room.
Seek a Way Out
Take the gas torch from the right.
Open the lockers and get the goggles and the toolbox.
Equip the goggles, then look at the poster. There are some circled letters.
If you look at the dust chute to the right of the locker while you are wearing the goggles, you will see two screws and a screwdriver.
Go to the slider panel on the console in front of the incinerator and slide it to show the letters from the poster. The letters are:
When the correct letters are entered, the windows into the incinerator will open.
Touch the yellow window to switch to Phi. Look in the round openings to find a screwdriver.
Equip the screwdriver and use it on the metal panel below where you found the screwdriver. The wall has a number on it.
Use each screw on the scale to the right. Then use the screwdriver on the scale.
Touch the yellow window to switch back to Diana. Go to the dust chute to the right of the locker and enter the total weight of the screws and screwdriver (see above). If correct, the dust chute will unlock.
Put the toolbox into the dust chute and have Phi use the screwdriver on it. Then touch it to start a puzzle. Choose a tool to put it into the puzzle. You can rotate each tool by tapping it multiple times. When you solve the puzzle, you get a note.
Put the gas torch into the dust chute, then touch the yellow window to switch back to Phi. Have her use the torch on the thermometer to the right of the scale.
Touch the yellow window to switch back to Diana. Have her check on the external thermometer below the incinerator windows. She can take the coin. Have her use the coin on the grating that covers the red button. Then press the button. A chair appears. Touch the chair. Sigma gets stuck in it. The box with the revolver comes down.
Take the revolver box, then use it on the dust chute. Touch the yellow window to switch to Phi, then have Phi use the screwdriver to open the revolver box.
Now switch to Diana and touch the top of the chain to pull the revolver box out. Use the revolver on the box to the right of Sigma. The room escape ends.
Now you must decide whether to pull the trigger or not. After you make a decision, you can always use the Flow menu to go back and find out if a different outcome is possible. If it really is random, you might have to try several times to get a different outcome.