Idea #1 – Use red light from below and some crumpled old red & yellow gel on top with some half-burned logs scattered around. Too realistic a fire effect is a distraction from the acting. If anyone notices or remembers the fire you overdid it.
Idea #2 - Play around with fluorescent starters (if you can find them these days) in series with the incandescent lamps or gelled lighting fixture. Provides a very nice, random, somewhat realistic flicker type flicker effect.
Idea #3 - A couple of things on starters that I've learned over the years...
1.) Always have one constant circuit as it makes the flickering fire look more realistic.
2.) Use the FS-2 starters. They should be available at your local electrical wholesaler.
Idea #4 - Go to the local fireplace store and borrow an electric insert that's designed for inside a real fireplace (cost to purchase about $150). Insert consists of smallish bulb lighting a wooden frame holding red/orange/yellow gels and a tinsel-looking thing that rotated to make a crackling sound.) Mount it on a caster dolly frame for ease of moving off and on stage. Arrange remainder of stage lighting to make light seem more "real". (i.e., very little down light, smallish lights behind the "campfire"/front light aimed to actors who were upstage of campfire, darkened but not black area lighting... embellish as you wish.) Surround with small logs borrowed from friend's firewood stack (fire marshal OK’d for brief use without requiring flame proofing, had stagehand remove immediately with offstage supervising the entire time, extinguisher within reach, fire marshal rep onstage in wings also). Looked fine, no hazard.
Idea #5 - I put a small trap into the stage floor (where the trash can would sit) and drilled about 30 1/4" dia. hole in the trap so that light and smoke could come up from below. I cut most of the bottom out of the trash can, and put in screen wire so that anything that went into the can stayed in. The effect was simple and safe (no fire).
Idea #6 - The last time I did this we were able to mount a small Rosco-fogger directly under the stage in the trap room and pipe it up through a small hole in the stage. The campfire unit itself had an open base so that the smoke/fog would drift through. It worked great.
Idea #7 - We pulled a trap, replaced it with one that had a few holes drilled in it, and sent up light and smoke from below when Lenny and George were huddled around their "campfire." The rest of the time, it was just another section of floor.
Idea #8 - Fuel was GAM torch pellets (usually two at a time). These "pellets" were first placed into chaffing dish sterno holders (those little metal tuna fish sized cans with sliding lids). These were then placed in the "scenic" steel drums or in a cement board lined box sunk into the stage. Actors slid the lid(s) and used a match to light the pellets. Yes actors were able to do this. We had people manning fire extinguishers on both sides of the stage.