I've used Flitz but never on a highly polished finish, only on a brushed stainless finish. For that purpose, it was outstanding. This was for an "idiot mark" on a second-hand 1911. It was pretty bad, so I used 800 (I think; it was 800 or 1,000) grit sandpaper and a little oil first to do the deeper part of the work. Then I followed that up with a gentle application Flitz to blend in the light sandpapering.
Like Barnett said, I think any of the options he noted would work. But I wouldn't start there with a deeper scratch because I think the key is to do the initial work carefully and keeping the direction of the material removal exactly in line with the brushing, or grain, of the finish. I used a sliver of sandpaper wrapped around the end of a small, flat piece of metal. Slow, light, and short strokes. The gun oil was to not only help with the friction but to help prevent any new scratching from tiny metal filings as they come off.
There was also a scratch, but a lighter one, in the tapered part of the trigger well below the full idiot scratch. The direction of the "grain" there didn't allow the sandpaper, so I used Flitz only. I put the rag over the eraser end of a pencil, Flitz on the rag, and did a bunch of light, with-the-grain strokes to get the scratch out.
The final result wasn't perfect, but someone would have to look awfully close to find the old scratches, like magnifying glass close.