You shouldn't flute your barrel. If your barrel is too heavy, you should send it to me right away!. Only I can dispose of it properly. I won't even charge you for it or anything.
My dad used a big SAIMP (~65" Table) Hydraulic Tracing mill to do the work with carbide woodruff cutters. It was all he used that mill for: He made several follower rest towers and pads for the opposing side of the barrel to minimize/eliminate flexing... and tracing patterns cut to match the barrel contour for the stylus to follow. I spent many an hour running that thing: we never took more than about 0.005" when starting a flute, and never more than 0.001" or 0.002" when the cutter was at the finished depth - when cutting radiused flutes it's important to remember that as you cut the flutes deeper, the cutter removes more material and you need to need to back off how much you cut on a manual machine... Bill Wiseman of Wiseman Barrels and Ballistics would take it a step further: When fluting a barrel, he would cut one flute, then rotate the barrel 180 degrees and cut the opposing flute until the barrel was done. (American Rifleman, June 1986: a Heavyweight Elk Rifle) Of course, if you had an odd-number of flutes, this plan would need to be modified. I'll get some pictures of the setup.