Poorboy may be correct: that vintage extinguisher may plated brass, not solid brass.
Judging by the patina (IE, color of the faded/corroded material from time) you may have a copper-coated extinguisher.
Either way, using a brass or copper-specific metal polish is highly advisable, as either of these metals are "softer". I would be very leery about using chrome cleaner on them just because I have such a chemical on hand. I would suggest using MAAS metal polish for either of these metals. Also, as mentioned above, using soft cotton cloths. like cloth baby diapers OR chamois-type soft nap microfiber are highly suggested for both application and wipe-off. It`s a very dirty job and I would wear latex gloves if you do not want your hands to be black for a few days after polishing.
If you have access to Dremel Tool and wool-or-felt polishing bobs (or fobs) of various shapes (balls, cones, and cylindrical) , this can make polishing tight areas much easier with great results rather than doing it by hand with cotton swabs (AKA Q-Tips), which tedious as well. I see that Top-of the-Line Detailing sells a3" wool mushroom buffing ball for buffing metals that has a solid shaft that fits a cordless drill chuck that may make this polishing job much easier, as well.
I would not suggest taking it to a chrome shop and having them "buff" it out with a fixed polishing machine (think pedestal grinding or sharpening machine) and a wool pad, UNLESS they have soft metal-specific pad and polish. Polishing/buffing chrome or aluminum or stainless steel is one thing; brass or copper is another.