Instead of Flitz, I'd use JB Bore Paste or JB Bore Shine.
Flitz is an embedding abrasive, and is coarser then the non-embedding super-fine abrasives used in JB.
The problem with Flitz is that the abrasives embed in the barrel steel, and when the bullet passes down the bore, it acts like a lapping slug. This can oversize a bore and rounds off the necessarily sharp edges of the rifling.