One of the theries behind the fluted barrels is it makes them more rigid.
Not true. By removing mass, you removing rigidity.
The x-sectional area is what rigidity is all about.
Have you ever seen a fluted barrel on a BR rifle?
You can lighten a heavy barrel by fluting but it does not make it more accurate or more rigid. Yes they cool good if the flutes are deep enough. I have yet to find a real good excuse for a fluted barrel., and I can easy do it myself.
But if you think they look good,then by all means get one. Myself I like an octagon barrel.
There is a theory about them too by removing weight and still retain a better x-sectional area than a round barrel of equal x-section because of the two radii.