I've never seen scratches removed 100% from chrome rubbing all kinds of stuff on it.
I've read about some chrome shops being able to polish scratches out of chrome but never seen it. Did some Googling on the topic and found some info.
Here's the problem, first the actual chrome layer is very thin, so you don't have a lot of material to work with. Next, in order to actually remove a scratch, you don't remove the scratch, or scratches, you remove the material surrounding the scratches in an effort to level or flatten out the surface
. This circles back to the problem of the actual layer of chrome being thin.
Then next problem is chrome is hard, this means it doesn't lend itself to be workable or abradable easily by hand or machine.
I've had a lot of people over the years bring cars to classes I've taught and shown me scratches in every conceivable "material" or "coating" ever created and when it comes to chrome, real chrome, not plastic chrome, to this date I've never seen anyone live in front of me apply something and remove 100% of all scratches. I've also never done this myself.
I would also point out that most people that have had the problem of scratches in chrome, when looking for an outside company, person or product to solve their problem, their standards have been perfection, as in, if you attempt to work on their chrome doodad, whatever it is, they expect to see 100% perfection. If you don't hit this mark, not only are they disappointed, they often have the attitude that if you rubbed something on their doodad and it's not better, now you're responsible for fixing or replacing the doodad.
Not sure where this type of thinking comes from but it's taught me not to rub polishes on already scratched chrome surface for other people or even give them something to try to rub out scratches on chrome surfaces because if it doesn't work, and especially in a worse case scenario, it instills scratches into the chrome, then you're back to being liable.
If you own something that's chrome and it's very important to you, do some research first, maybe contact a "real" chroming company and see if there's any real solution to the problem. And, as a safety measure, always test products in an inconspicuous area and then inspect the results.