It will work. Flexi internally doesn‘t manage cut contours by colour name, but when using the cut contour tool, it defaults to a contour colour which is correctly named for use in third party rips. If unsure, you could select a spot color named „CutContour“ in the design centrals color chooser while applying a cut contour.
If exporting to PDF, be shure to uncheck „surpress options“ and look if the export of contour lines is enabled or not.