The major diameter is 1.238". If you want to verify, buy a 5C collet and measure it.
I am guessing that the thread form is 60 degree included angle.
Most of the major threading insert manufacturers provide tables showing the infeed for a particular pitch and thread form.
Below is one example. Another very good one is the Seco one:
https://www.mitsubishicarbide.com/application/files/5314/7191/5783/tec_threading_depth_external_en-us.pdf
Use the numbers as a guide. The final dimension you require depends a lot on the cutting tool you use – a hand ground HSS one will be different to a multi-pitch insert (A, AG, G, etc.) and will be different to a single (specific) pitch insert.
If you are set on this route, it might be wise to buy your collet set and cut a test piece in the same material as the real version to verify that it fits every collet. If you cut the final version to a set of numbers, what happens after the chuck is assembled and one of the collets does not fit?