As their name suggests, the Flame Behemoths focus on fire to attack, which can melt away small Vek to make up for having very little direct damage early on. Having more enemies on fire is essential as it allows the Flame Mech to deal heavy damage.
Ignite tiles that vek are emerging from and they will be on fire once they appear.
Prioritize movement and additional range upgrades for both the Swap Mech and the Flame Mech first, as they greatly improve the Flame Behemoths ability to reposition enemies. The Meteor Mech already excels at this from the start, and can remain un-upgraded for the majority of the run.
Fire won't damage buildings, so you can freely target them with the Meteor Mech to push vek away from them, or shoot through buildings with the Flamethrower (once its range is upgraded) to hit and push Vek behind them. Not that this is not viable once the Meteor Mech's +2 Damage upgrade is obtained.
Fire does not damage buildings, trains, or the bombs, but does damage other items with hit points you are supposed to protect that are not immune to Fire; such as the Disposal Unit, Terraformer, Earth Mover, etc.
Enemies that are on fire take damage before they perform an action, so the Flame Thrower and Vulcan Artillery can effectively do one immediate damage even without upgrades.
Vek that aren't already burning won't deliberately stand in fire, so you can protect structures from melee Vek by igniting the tiles around the structure.
Use the Swap Mech to drop land enemies into water/lava; or to pull guarding targets next to deployable tanks.
Destroy the Dam missions are tricky until you power up the Vulcan artillery. It can't be set on fire, so none of your attacks can damage it. Look for opportunities to push Vek into the dam or redirect their attacks toward it. Consider avoiding this mission entirely if lacking alternative weapons.
Vek that are at 1 HP and die to fire damage at the start of the enemy turn still contribute towards the maximum enemy count at one time on a mission.
Ice on Pinnacle Robotics instantly breaks when attacked by the Flamethrower or Vulcan Artillery, which is key to disposing of Alphas.
Be careful if you have Advanced Enemies on, as there is the possibility of encountering the Smoldering Psion, which silences the entire squad's firepower.
While it looks enticing to obtain, Heat Engines is a near-worthless ability as the Flamethrower can only damage burning enemies - the only benefit is that it deals three damage and the downside of eating up your own fire tiles outweighs this.
Some pilots work very well with this squad:
Kazaaakpleth as a starting pilot not only grants the Swap Mech attacking power but is also the only way of directly destroying the Dam.
Chen Rong and Archimedes help the Swap Mech survive after using its ability.
Mafan on the Swap Mech or Flame Mech immediately increases their range with his included Reactor Core.