No time to learn like the present. You should be able to cut the thread and use the chuck to test it for final size. You can make it a bit on the loose fitting side if the spindle uses the usual method of a stepped collar that does the locating. The thread is just there for retaining purposes.
To get best concentricity you should make the other end of the false shaft first and press it or weld it to the D13 flange. Then mount that on the spindle and turn the business end with thread and collar in situ.
Get some material and make some test pieces up for practice, cutting the thread etc.
If you are not confident of your skill levels, you could hold off until you have more experience.
For the time being, simply hold the body of your step chuck in the jaws of your regular three jaw chuck (or four jaw if super fine concentricity is essential). This would be good enough for most flat washer type jobs in the hobby workshop.