You are going to need to print on white and then contour cut out your design to get the desired effect. Mutoh does not make a printer that uses white ink.
Your settings in flexi appear to be correct, although it will ultimately depened on the color profile/preset that you are using. FYI, most of the ones you find on the web and download don't work all that great.
Spot color printing / color matching is not much fun. All your spot colors will convert into their closest 4 color process (CMYK) equivalent. This will mean that spot reds and blues will be tough to get to output.
You need to turn off the spot color mapping unless you are specifically trying to map one of the spot colors in your drawing to a particular ink color. For example if you draw something with a spot black in your drawing, then turn on spot color mapping, and then select the black to map to the black ink... you'll get a pure black print. This can save you lots of ink when printing black text for example.