I have owned three Remington Milspecs. After break in all shot .25-.5 MOA 5 shot groups. Many times even better. They would also hold accuracy for 150-200 rounds and clean quickly. I think this is the main advantage of the MilSpec barrel. The break in I used was:
Using 43 gr. Varget, 210 Fed Match primers, 168 SMK, Fed Match or Lapua brass, OAL 2.81".
Shots 1-10, Clean after each shot.
Shots. 11-23 Clean after 3 shots
Shots. 24-42 Clean after 5 shots
Done
After about 7 or 8 shots of the first cycle you should notice that the carbon cleans up noticeably faster. I think this might be over kill, but I took advantage of some load or ballistic work. For cleaning I used a couple different solvents which all worked fine.
The Bore Tech CU +2 is my favorite. I. Ran one or two wet patches, then nylon brushed about 10 strokes, then back to wet patches until clean. Dry bore. Shoot. Get about 2500 rounds before my groups start to open about .25-.5 MOA larger, but I have shot pretty hot in competition.