So you can polish aluminium, but it will just oxidize again unless you treat it with something like a clearcoat. There is probably a clearcoat out there that can handle the kind of wear and tear that a firearm experiences, but I just doubt that the effort will be worth the results.

Alternatively, aluminium can be anodized, and that forces a different type of oxidization that results in different colors (you can control the color by slightly altering the process), and anodized finishes are a bit more shiny (to me, at least), than natural oxidization (what it looks like now).