I’ve achieved excellent results using FlatCAM to generate and AutoLeveller to post-process PCBs routed in KiCAD: Nomad Level Calibration
I haven’t explored Carbide Copper thoroughly because the FlatCAM workflow works so well for me. I suspect that at least part of your issue is that your EDA tool isn’t generating thermals (those are the links between a pad and a copper pour) in a way that Carbide Copper understands, either because the shape in the gerber is unsupported or is too small to mill effectively.