You can use Inkscape as your design program and save the file as either SVG (better) or DXF (good). But you need to create the toolpaths & then the G-Code before you can have Mach3 take over.
Fusion 360 or Sheetcam for the toolpathing and G-Code generation and then to Mach 3 and the Crossfire.
So your workflow would be:
Design in Inkscape → Insert SVG into Fusion, create Toolpaths, Generate G-Code → Open .tap file in Mach3 & cut.
Or swap Sheetcam for Fusion. But you need Design, Toolpath definition, G-Code generation and machine control. Inkscape can do design, Mach3 can do machine control but you need another application to do the bits in between.