I don't think I would do that Hans. First, I am doubtful that Flitz is made to be used like that. Some folks do "polish" a new bore with Flitz on a patch and seem pleased with the results, others don't and seemed pleased with their results. There are kits you can buy that are formulated to do what you are considering with other abrasives. But, do you really need to? Is it accurate and easy to cllean already? I have read of a variety of results with fire-lapping. Opinions vary a lot on breaking in a new barrel, or manually lapping/polishing it right off the bat. If it's a good barrel and finished well, a lot of times it will shoot and clean just fine right off. Shoot it, clean it correctly after or during a range session. (Lots of opinions on shoot/clean/shoot/clean sequences - won't go there) You won't hurt it. Just clean it correctly without dragging a lot of crud through the barrel or dinging the crown. That's kind of the conservative approach, but as one barrel maker puts it - it's made to shoot and clean the way he makes it - why start polishing off the edges?
Just my opinion, who knows - maybe you have a great idea there. I'm just saying I would have some doubts. Good shootin'.