I think others have reported success with the vinegar/salt method. If the chrome is loose and flaking it's going to come off anyway. You can also try Evaporust. A lot of these methods will convert the rust to black oxide and the part will need repolished afterward but as far as I know they're all pretty safe for chrome.
I have a buffing arbor and wheels so I generally just wire brush then polish parts that need it. I don't do a lot of chemical rust removal.
If you're going to be cleaning a lot of rusty metal I recommend a set of buffing wheels and the different compounds.
Steve here has had very good success with a brass wire brush and Brasso for cleaning metal. 0000 Steel Wool is a good choice too.
Rodney