Most manufacturers of gun barrels today run the barrell contour and the threads on a CNC lathe. The threads can be gaged with hard tooling gages such as GO/NO-GO gage or on a Computerized Measuring Machine, CMM.
The manual lathe machining operation will usually use the Three Wire method of measuring which requires calculations using the standards as published in a Machinist Handbook. The purpose of running the thread on a lathe with a single point cutting tool is to insure longitudinal alignment. Cutting the thread to 90% in the lathe and doing the final adjustment with an adjustable split die allows the smith to adjust the thread to a close fit with zero lateral movement on final lock up. Clean and well lubed threads should require a wrench for the last several turns for either a muzzle brake or a suppressor. The longer the attachment, the more critical the fit.
The chasing of the lathe turned thread with a split die is performed by setting the die to a standard such as a tap or a factory thread on the large side and then adjusting to the the split die to the required fit. With practice the average person can faciitate the correct fit with two or three adjustments of the split die.
Go slow, use caution, and practice on scrap stock. It's cheaper than a new barrel.
The HEX threading die is used for chasing damaged threads. Not recommended for close tolerance work!
The ACORN threading die is used for production work and loose tolerances.
Enjoy the journey.