Agree that it is on a case by case basis, but caution is advised when burning inexpensive furniture. This chest does look like it is made of plywood, but even there the ply adhesives aren’t intended to be burnt and inhaled (now if we made it out of hemp… hmmmm… throw in a USB charger and now you are talking!) A rude sort of fume hood can be made with a fan, a window that opens to the outside, scrap cardboard, a bit of duct tape and some cursing. Slow down the flow by covering parts of the intake or McGuiver a rheostat in there or something. Make an Arduino project out of it.
Just trying to be the safety nerd.
Still this is a beautiful piece and this is the sort of thing i love seeing here on BB!