Don't get set on fire?
But seriously, the thing that makes them dangerous is their move Wildfire that adds 14 fire DoT to an already burning adventurer.
There are a few moves that can remove fire damage, like the Cleric's Bless or the Ranger's Field medicine. Having your Cleric always bless the one hit by wildfire should really help your survivability.
The other thing you can do is to bring a lot of Holy Water when you prepare and use it if your adventurer is on fire at all, that way the fire slime don't get a valid target for wildfire.