There is no "break-in" required on chrome-lined barrels or for that matter, any barrel.
That said, (and given that many STILL believe in the "fire a round/clean, fire a round/clean philosophy") here's what I do with a new barrel, no matter what it's made of , no matter whether it's a $50 dollar gunshow special or a $300+ dollar Krieger barrel.
Fire 10-20 rounds, properly clean barrel, shoot 20-60 rounds and then properly clean barrel again...... after this clean rifle when done shooting.
FWIW, here's a cleaning method and products, there are many.....
I use nuthin but Sweets 7.62, SuperTech 2000 Carb-cleaner from Walmart and Break-Free CLP, always make certain ya clean the Sweets out if ya use it, that's what the carb cleaner is for, as Sweets is a serious ammonia based product which can do bad things to your barrel, should ya space out and forget it for a day or two, always flush the Sweets out completely, if your going right back to shooting ya don't need to lube/oil the barrel, just give the carb-cleaner time to evaporate.
I like to perform this cleaning while weapon is [b]WARM[/b] from shooting, note: I said warm, as I use nuthin but NYLON (which is why warm, not hot, or ya get a melted mess) bore brushes in my barrels, no matter the caliber and cleaning while warm really makes the Sweets work well, it usually only take 2 sets of brushing bore to completely clean bore of bullet residue/copper.
How I clean: with rifle benched, upper tipped up/separated from lower at takedown pin only, pivot pin still intact, install bore guide, place rag over scope if ya got one on rifle and over stock where upper is separated, rest upper w/ bore guide install on lower, where rag is, as bore guide will rest on lower, place Dewey rod w/ nylon bore brush into bore guide, slide till in throat of barrel, tip rifle up, pour Sweets in from muzzle, holding finger over end of barrel work rod in easy, back then in again 2 times, to get a good soaking of brush in the Sweets, move/reposition to back of rifle, with down and back counting as 1 stroke, stroke vigorously 40-50 times. The Sweets 'cus barrel is warm, will froth profusely, if your shooting moly coated bullets, this will be a bright blue froth, but even naked bullets create a blue/greenish tint to the froth color, when stroking is done, remove rod, using little red tube supplied w/ Carb-cleaner, insert into bore guide and flush barrel completely of Sweets. Run one dry patch, generally, not always, there will be a greenish tint marking on the patch, this is indication of copper still in lands, repeat above process and give her 40-50 more strokes, this will normally have bore clean. Once re-flushing w/ Carb-cleaner is done and patch comes clean, remove bore guide, tip upper up and insert little red tube into the gas tube, "watch your eyes", but spray carb-cleaner into gas tube, THIS REMOVES ALL VESTIGES OF THE SWEETS, which probably got in there while cleaning, as it's a serious bore cleaner, ya don't want to put rifle up with Sweets anywhere, IMO, as aside this also cleans out your gas tube and keeps it that way, (as if the enormous pressure of firing doesn't do a good enough job) the spraying into the gas tube is just for complete removal of the Sweets, so ya know.
If your done shooting, CLP the rifle b/bc/ch, trigger and bore, run a couple patches to remove excess CLP in bore and store rifle. If your going back to shooting, I don't CLP the weapon, just button it up and go back to blasting.
This is what I do and how I do it w/ every rifle I own, I learned thsi method from someone, who currently builds our rifles and got us into long range shooting, someone I trust and respect.
YMMV,
Mike