I don't have any experience with cleaning really dirty chrome wheels, I just used P21s wheel cleaner back when I had them, and I never let them get that dirty.
Chrome's pretty tough stuff so you can pretty much trust any normal wheel cleaner to be OK on it. A product made specifically for chrome wheels will probably be a rather strong cleaner and might be more than you need for regular cleanings.
Products like cleaner-waxes, AIO, etc. oughta be good to clean them. I'd use AIO+SG myself and then just clean with carwash shampoo.
IMO the big thing with chrome is to avoid scratching it. I'd also avoid harsh products just on general principles. Once you mess up chrome (in any way) the only solution is to replate.