I don't know all the reasons why they flute revolver cylinders..
Looks are very important to firearm sales. Fluting cylinders can add some elegant lines.
Functionally, there is a value in more uniform wall sections. Particularly for heat treating.
Thin sections quench or cool much quicker than thick sections. That can cause cracking .I don't know about revolver cylinder heat treat,but I have seen non-uniform cross sections crack in heat treat.
I don't doubt there is advantage in reducing rotating mass.
Overall weight matters. Aircraft and race vehicles are lightened at every screw,hole and detail because every bit adds up.
Done right,there is SOME potential to optimize the tradeoff between weight and rigidity with fluting...
But its good to look at the whole rifle. How often is a "light" rifle compromised by bolting a 50 mm + objective astronomical telescope on top.Maybe using a 2x to 7x variable instead will save as much weight as fluting.
Dumping the Mauser type steel guard and floorplate/mag box in favor of a blind magazine and a Rem 700 ADL aluminum trigger guard is a chunk of weight.
A vacuum bagged,foam cored Kevlar and glass epoxy stock can weigh about 20 OZ. A laminated hardwood stock is heavier.
A barrel is a big piece of steel,and it seems the obvious place to save weight,but the barrel is key to accuracy. I suggest not getting tunnel vision on lightening the barrel.
I don't know all the tech details of composite or aluminum sleeved barrels.
An obvious bug to work out is different materials have different coefficients of expansion. Thats how a bimetal strip works. They change shape with temp. Thats how some thermostats,circuit breakers,etc work.
I don't know Bartlein's profile code. A 3 or 3A profile conjures up a vision of a standard Remchester 30-06 hunting rifle barrel. Which,FWIW,is probably a good compromise. Stepping up to a 300 Win Mag will likely get you a #4.
These contours don't have all that much extra steel to flute.....At least as far as removing weight. You can make token cosmetic cuts. A .030 or .040 depth of cut will look fluted,but remove very little weight.
IMO,you start getting into the target contours before there is enough steel to effectively flute to make a weight difference.