SG, the only thing to watch for is barrel taper. There seems to be a need for a min amount of material around a bore to maintain accuracy. Depending on who you talk to, it ranges from .18 to .27 in on either side of that bore.
If you are fluting a tapered barrel, they are unlikely to reduce depth of cut as they progress down the pipe so will likely set at the shallowest cut. That reduces the benefits at the 'big' end and reduces the fluting to merely cosmetic.
If they set the milling to cut too deep at the thin end, you may get bulging which is not good for accuracy or safety.
I look at fluting as a great way to balance weight with rigidity. I feel the rigidity of a fluted barrel is better then a 'thinner' barrel of equal weight. All you stress engineers can tell me if I am right or wrong.
The appearance is nice too but for extra cooling - not really significant.
Jerry