A recent discussion on the topic,
http://www.snipershide.com/shooting/snipers-hide-bolt-action-rifles/183467-barrel-fluting-%3D-poi-shift.html
Per that discussion:
- testing has shown that fluting can negatively impact the accuracy of a barrel. There is no guarantee that it will, but it has been shown without a doubt that it can have impacts on the barrels performance.
- most worst case scenarios are fluting a button rifled barrel, especially if the barrel was not properly stress managed/relieved.
- barrels that are run hard and go through full thermal cycles are most likely to exhibit problems, versus barrels that are shot at a slow/measured pace and do not have a lot of heating & cooling cycles.
If you have a properly made barrel with cut rifling and the fluting is done properly with stress being managed throughout the process, chances are you will end up with a good barrel. On the other hand if you have a barrel with stress in it, then fluting can cause issues.
Personally, I am going to use the barrel profile that works for what I need, if I do that, there is no need or benefit to the fluting. Sorry, I shoot my rifles for performance/results, so the "looks thing" is not on my radar screen.