I own a couple of Bartlein barrels for deer rifles in 6.5-284. I asked them to flute the blanks and they came up with the poorest excuse for fluting you ever saw.
Many barrel makers lack experience with hunting rifles and the idea of a light barrel bothers them. Rock Creek has done the best job fluting a hunting barrel, I also have two by them, a 6.5 WSM and 6.5-06 Ackley. They will flute their #3 which is a pound lighter than Bartleins and of course, has a smaller contour. The Rock Creek barrels are the lightest I own. The rifle weighs 7.5 lbs with a 2.5-10 Sightron in Conetrol rings. With a 26 inch barrel it is as light as I want to wave around at game animals. I backpack and Xcountry ski with the rifle for deer.
I have several Krieger barrels but they start at #5 for fluting. I like their 10 groove for varmint weight barrels but not much for weight reduction.
Recently I had a McGowen barrel blank fluted at the factory. I was disappointed. Shallow flutes and short length.
Shilen does not flute barrels.