I just completed a barrel break-in for my Sweet 16. Barrel break-in procedures are like opinions - everyone has one. Most importantly, clean after a single shot for the first 8-10 shots. Then clean after 3 shot groups - fire as many 3 rounders as are necessary. Your 416 SS barrel shouldn't require as many shots as a chromoly steel barrel so there's really no need to overdo it. My procedure is as follows: (I prefer a "wet" break-in using Militec-1 and bore paste, some don't, but I know that Militec works. You will however use a lot of Militec when breaking in a barrel so the choice is yours)
Before anything else: Invest in a good cleaning kit (stiff coated rod - I use Dewey), get plenty of quality patches, jags, and brushes. Get a good solvent, bore paste or copper solvent, and some Militec-1 or Kroils if you decide on the "wet" method.
1) MOST IMPORTANT - start with a CLEAN bare steel bore. Clean with a good solvent and patch dry. Your barrel is clean when the patch comes out perfectly white.
Here's where the Militec comes in - I run a wet patch with Militec down the CLEAN barrel before each shot. Now fire your weapon.
2) Clean your bore. (Use something that gets the copper out - I use bore paste, others use Sweets or something similar, and clean until the copper is gone). I don't like waiting for the copper solvents to work - most take at least 5 minutes - this multiplied times the number of shots you will fire will make for a very long day at the range. Hence, I prefer the paste.
Now I repatch with Militec again, and everytime before firing a round through the CLEAN barrel. The heat and friction of bullet travel makes the Militec work - it bonds to the metal and subsequent applications only enhance its ability to lubricate, protect, and repel fouling. Again this is only my opinion, but my weapons' bores treated with the stuff clean easier.
Keep firing single shots until you notice that it requires fewer applications of the bore paste or copper solvent to expel the copper. (you can actually see the copper on the patch when you use paste, if you use copper solvent, the patch will be blue from the reaction.)
Let's say it's been taking you three patches to expel the copper on the first eight shots, but on the ninth, the second patch comes out without copper. Now you can move to firing 3-shots before cleaning.
3) Fire 2,3, or 4 more 3-shot groups - You should notice that after each 3-shot group you bore becomes easier to clean than before. There's no set formula for determining when you've reached the break-in point. I look for less copper on the patch. My last break-in required 7 single shots, plus 2 - 3-shot firings, and I fired a 7-shot to complete the firing process. After the 7-shot firing, my bore cleaning yielded less copper and powder fouling than the first 3-shot firing. YES - this is time and ammo consuming, and I'm sure someone will say that I did it wrong or didn't need to do it all. Every barrel is different, but this barrel is mine and that's how I do it. Good Luck.
You can also check out Krieger's site and HighPowerRifle for "expert" break-in technique.