Stretch that drill bit

[Toolmaker51]

Not to dissuade you, but button rifling is a bit more complicated. 1st; you asked about a broach. For this type of cut, it is a cutter with multiple radial teeth. They each 'scrape' a small bit of material, with an increase in tenths [.0001] from the starting end. It requires accurately sized and straight bore. It would take a 'set' of them, each with an un-toothed section to engage the previous cut and rate of twist. 2nd; A button is carbide, which requires specialized grinding equipment. Neither a practical project.
Best solution is a hook tool. They go back centuries and certain 'cut-rifling' barrel makers still use them. The bore-riding portion has a slot and adjustment for the cutter. It carries the cutter as being pulled through bore. Twist is regulated by the rifling bench. A pass is made in the first groove, rotated around to each groove one cut at a time. It has a wedge to increase the depth for each cut. .003 depth per side would need about 30+ minimum passes in each groove. The best barrel makers including Colt, Pope and others could control size so well the result was a very small taper - larger at breech than muzzle - to compress a lead projectile gently for the greatest accuracy. The debate goes on which method produces the best barrel. Cut rifling has the sharpest grooves and lands. Button barrels have the smoothest surfaces, burnished by the button, and easier to clean. Cut is great for lead, button barrels are good for jacketed bullets.