Polylines should work fine. There are bugs that were fixed shortly after the very first 4.0 release. Genuine arcs are used, not approximations. This could cause problems when importing to copper layers since arcs are not allowed on copper layers. Another problem you may encounter is that KiCad will use either 16 or 32 segments per 360 degrees to approximate an arc in the manufacturing output files; a consequence of that is that large arcs will be wrong in the Gerber files even if they look OK in the mechanical exports. Yet another problem which I encountered was that circular copper pour regions are somehow recognized as being circular and the numerous short line segments representing the region are replaced with 16 or 32 points and of course violating the intended design.
I would have to have a closer look at the DXF file to see what is going wrong. Maybe the entity is an 'arc' and perhaps that's still not supported in the importer. In the dialog shown by Joan_Sparky, try by clicking on the "Merge Profiles into Polylines" and see if that makes a difference. The DXF importer is extremely basic and gets very little attention.
OK, I had a look at the file and it used PolyLines. I need to find some time to find out why this is failing.