Peter, can you measure the angle of the splines, some are just cut with a 60 degree cutter, test with a 60 deg thread tool to see if it fits. If it does you will need to count the number of cuts to make and calculate the number of handle turns on your rotary table to use between cuts. One way to get the depth of cut is to measure with the blade end of a caliper across opposing grooves and then deduct that from the OD, divide by 2 to get the depth of cut.
You can buy various angle cutters or maybe make your own from a broken HSS centre drill/slot drill/milling cutter, fitted into a shank and held with a grub screw.
You would use this tool in a collet in the vertical spindle.
Emgee