Tried 2022 rulebook, companion guide. Nowhere can I find what is the recommended skill check to extinguish a fire.
Mild spoiler alert: The very first scene of The Fall of Tinath (published 2017 and released with the Core Rulebook as part of the Traveller Starter Set) has a situation where player characters need to contain and extinguish a fire on the ship they are on. The main purpose of the scene is to familiarise new players with the task system for Traveller.
Fighting the Fire: Everyone who is trained for a job aboard a starship learns how to deal with fires and other emergency procedures. Travellers may therefore use their highest skill out of Astrogation, Engineer, Gunner, Pilot or Steward to deal with the flames. Anyone who fails the check suffers 1D damage from heat and smoke, and runs the risk of the fire spreading. Note that rolls to fight the fire are also subject to the same penalty as other tasks whilst the ship is on fire. Thus, the first attempt to put the fire out is at DM-3. Firefighting: Routine (6+) (relevant skill) check, (1D minutes, END).
Succeeding on a test reduces the Fire Value by 1 (it starts at 3 in this scenario and is extinguished when it reaches 0), while failing a test has a 1-in-3 chance of increasing the fire value by 1.
There may be further rules on firefighting in Special Supplement 4: Rescue Ops (published 2014). I do not own a copy, but looking at the last page of the preview on DriveThruRPG, the Service Skills table for the "Rescuer" career (which includes firefighting) lists the following skills:
- Vacc suit
- Physical science (any)
A character who has done their first term (basic training) in this career will only have level 0 in each of these skills, which presumably includes how to fight fires. The presence of Battledress on the list (which is no longer a separate skill in the current version of the rules, being subsumed into Vacc Suit) suggests that this career description is only for rescuers on very high tech worlds - see speculation below.
The following are my personal opinions. The Fall of Tinath rules are usable, but the referee should select appropriate eligible skill/s based on the context of the fire. For fires anywhere on a spacecraft or space station, I would definitely include Vacc Suit as a useful skill. (The failure to include Vacc Suit in The Fall of Tinath skill list is especially odd because the purpose of the firefighting task is to give other characters something to do while the pilot and engineer are occupied with other tasks!)
Obviously, the presence or lack of appropriate firefighting equipment and ability to access the fire should increase or decrease the difficulty of the firefighting task. Realistically, there should be a Profession (firefighter) skill that can be used for any firefighting situation, though it would be used so infrequently by player characters that it is understandable that it is not included in career skill lists - even ex-rescuers would consider it to be a "wasted" skill.
Ultimately it is up to the referee to earn their (generally non-existent) pay deciding the rules for any given situation. If the fire is in a TL4- settlement and the only effective way to fight it is to form a bucket brigade then it may be that Leadership and/or Tactics are the key enabling skills to get people organised, with individual heroic efforts using Survival or Athletics (Strength or Endurance). If the fire is in a TL15 metropolis with computer-controlled firefighting equipment then Electronics (computers) may be the most important skill.