Hello Blaster,
Flex cutting is really designed to cut straight lines, not curves, and there isn't a different way to cut the circles as you described. Flex cut will cut the vertical lines first and horizontal lines second and that is what is happening when the cutter cuts the half moon shapes. That is also why the cutter is jumping around when cutting the more complex gear shapes as well. Using a sorting function as described by P Wagner above can dictate the order of output for kiss cuts and reduce the unnecessary movements but it won't help when flex cutting.
There are some users here on the site who like to set their knife depth really deep and double cut shapes that have curves in them to get better results. Basically you would be cutting almost all the way through the vinyl and liner without completing the cuts so the shapes stay in the material during the cutting process but can be easily punched out when the cutting is complete. That is still an imperfect science, but your results on curves and circles will likely be better than trying to flex cut.
Best regards,
Phil Johnson
Airmark Corporation
(800)527-7778, ext 112
philj@airmark.com