It can affect accuracy in some cases. Probably more dependant on the method of rifling. Shilen for example advises against it; they use the button rifling method. Most hunting rifle barrels are hammer forged though so possibly okay. Of course, it depends on the skill of the gunsmith too.
If the fluting was done by the barrel maker at the time of production then it would be properly stress relieved. My Sako .308 Black Bear is fluted (they come like that) and is extremely accurate.
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