Re: Barrel fluting
Winmagman's right. Fluting a finished barrel will change its internal dimensions. Here's what happens.
Button rifled barrels will have a tight spot at the ends of the flutes and be a bit larger under the flutes.
Hammer forged barrels are the opposite of button rifled ones; larger diameters at the ends of the flutes and tighter under the fluted parts.
Cut rifled (single point or broached) barrels will change a tiny bit but not nearly as much as button or cut rifled barrels.
Having watched some fluted finished barrels air gaged with that great Sheffield device, the ball in the gage tube jumps as the gaging head goes past the ends of the flutes and lets more or less air get by it. Under the flutes, the ball stays pretty stable but at a different place than in the non-fluted part of the barrel.
And fluting a barrel removes steel that helps make it rigid. Fluting a barrel makes it less rigid/stiff than before. But a fluted barrel will be a very small amount stiffer than a solid barrel with the same weight per inch. Fluting adds a small amount of surface area that lets the barrel cool a bit faster; typically less than seven percent faster. A coarse sand blasted barrel will cool faster than a fluted one. If the barrel's properly stress relieved after rifling, it won't shift point of impact as it heats up; something fluting will not fix.
If you must have a fluted barrel, ensure its maker flutes the drilled blank before he reams it to bore diameter and puts the rifling it. Make sure its maker then laps the rifled bore and gages it for uniform dimensions before you get it.