This is an interesting topic. One which much folklore & hypermythology has been created (I just made that word up
The major differences you will see in whether or not fluting will effect a barrel is (in my sheltered world) a direct reflection of what type of rifling the barrel wears.
I have several Shilen barrels & they shoot awesome. Shilen (among others) are button rifled barrel. The material is displaced
by the button, not removed like a cut rifled barrel. So imagine a few spiral pressure ridges (for lack of a better term) running down your barrel. Now, start to remove material from the other side of the barrel... See how that COULD
create a problem? Think about the barrel density as the flutes (straight) pass over the area where the button has displaced the material during the creation of the rifling. Inconsistencies abound! At least from a plausability stand point.... Now there is going to be the gent that says "Hey! My Savage barrel is button rifled & fluted too! So phuey on you!"... take a a long hard look at your fluted Savage barrel (I have 2 & both shoot well). the barrel diameter is larger than a sporter & the flutes are FAR shallower than an aftermarket fluted bbl. I would imagine (I do that often lol) there is a very good reason for that procedure.
A cut rifled barrel having the material removed rather than displaced should not incur these issues as there is very little material "compaction" from the rifling process.
Clear as mud?
Fluting a barrel seems to be the modern version of Truth or Dare....
Button Rifled Barrels:
Can you? Of course
Will is hurt it? Plausable.
Cut Rifled Barrels:
Can you? Of Course
Will it hurt? Probably not.
PS- This is solely my opinion & a good bit of experience with Gunsmiths & use of both barrel types. This is not an end all for the discussion, merely my .002 - Enjoy