Torch lamp systems and flame lamp assemblies for producing swirling flames are disclosed herein. In one embodiment, a flame lamp assembly for providing a flame having a continuous spiral movement can include a plurality of spaced apart panels and a frame for supporting the panels to form a chamber for housing the flame. The frame can support the panels such that adjacent panels are spaced apart at panel junctions to create a plurality of air intake slots. The plurality of air intake slots can be in communication with the chamber to allow air to flow from an external environment into the chamber at an angle to provide vortical air flow within the chamber. The assembly can also include a burner assembly configured to receive fuel from a fuel source and to provide a fuel flow from a fuel release point to the chamber for ignition to provide the flame.