I used a buckle clip style design to make the model collapsible. (see third image)
The flames are designed to be friction fit but I also used a small amount of glue just to be sure.

Print settings:
I printed all parts with 0.2mm layerheight.
All the flame piesces were printed laying flat.
I printed the front part of the fireplace backside down without supports.
For the back part of the fireplace I printed it in its final orientation using supports, I also tried printing it backside down but this critically decreased the strength of the part.