I have broken in the barrels on many custom rifles that were benchrest rifles or custom P. dog rifles. All of these guns had Hart, Pac Nor, or Douglas Stainless Steel Match barrels on them.
The process involves shooting 5 shots, cleaning inbetween each shot, and carefully monitoring the amount of "Blue" on the patch after applying a copper solvent.
After 5 single shots, you go to 5 three shot groups, then 5 five shot groups, carefully watching the amount of "blue" on the patch after applying copper solvent.
What is unreal is that you see the amount of copper fouling start to really taper off somewhere between the third and 10th shot.
It is really a pain in the @ss to break in a rifle barrel, and I will never do it again, I just clean after the first 5 shots on a new custom barrel, then after 10 shots, then when ever the barrel needs cleaning. Breaking in a barrel is like going to the dentist, I really hate it!
Having said that, I don't think that you can ever break in a barrel that is a factory barrel, there are simply too many tooling marks in the barrel. I have seen most factory rifles smooth out after 300 or so rounds.
If you want to help your barrel out, then apply JB to a brush and swab your barrel 25 strokes with it, it will surely smooth out some of the roughness in a new factory barrel and will not hurt it at all. Flitz, on the other hand will remove some metal, and do not use it in a rifle barrel unless you want your lands that are normally sharp, rounded (learned this the hard way). Owning a bore scope can drive you crazy.
Rem Clean in the yellow tube is also a serious abrasive that will lap your lands round in your rifling. If you find that you have a rifle that is a copper pig, there are some bullet coatings that can and will reduce the copper fouling in your rifling such as (SPL) that Todd Kindler sells and Fastex. I have used Wax for over 20 years on my p.dog and ground squirrel loads where high volume shooting is taking place. I have very knowledgable freinds that swear by Danzac and they all have quit using Moly that builds up in the barrel.
The use of good brushes with a good copper solvent is all you need on new factory guns, and you should be prepared to clean the gun after 12 or so rounds, first trip to the range...you will get a load of copper out of the barrel after 12 rounds! Cleaning frequency will start to taper off as you get more rounds down the tube. Every barrel is different, and accuracy will dictate just how often you clean your rifle.
Accuracy is a relative thing, you will have to make up your mind just how accurate you want your rifle to be. Most rifles can be very filthy and still shoot 1 1/2" at 100 yards. Personally, I think that 1 1/2" at 100 yards is all the accuracy a Coyote hunter needs, your thoughts may be different. I strive to get my rifles to shoot 1/2" at 100 yards, but some sporter factory barrels just will not achieve that lofty mark.
I have never seen a Remington, Savage, or Ruger factory rifle that shot better with 100 rounds down the barrel vs 10 rounds down the barrel in regards to cleaning frequency.
Every savage that I have owned was a copper pig and very tiny groups were shot with all of them. The cleaning frequency was frequent with them, but the accuracy was simply outstanding, and that is an understatement. There was simply no way to lap the barrels on these rifles smooth, and I do make two different grades of barrel lapping compounds.
If it makes you feel better to lap your barrel by breaking it in, go for it. Fire lapping, however, is a very, very severe lapping process, and I would avoid it at all costs. Fire lapping is something that a guy does as a "last resort" fix. Fire lapping that I have done has lapped out .050 or more out of the throat, making it that much more difficult to reach the rifling when seating bullets.
Good luck!