I would start with the lightest abrasive possible, like Flitz, with a soft cloth and hand pressure, then work your way up as needed.
Photos of the gun in question would help, but the nickel plating is soft and using a Dremel and any kind of polishing attachment may take all the plating off, so start slow.
And I note this each time this question comes up - the black stuff that comes off with polishing is the nickel itself. Did I also mention take it slowly?
I agree. The only things I'd add are only polish in one direction. The grain runs from the front to back (different on Cylinders), NOT from up to down. I would also suggest disassembling the entire gun first. This is because you want as flat a surface to work on as possible with no protrusions to alter the angle you are polishing at. Anytime you can lay the 100% cotton or microfiber rag on a perfectly flat surface and move the part, that will assist in a smooth one plane finish. The other important reason you want to fully disassemble is so when done, all the Flitz can be cleaned off and nothing is left inside the gun and or its parts.
As murphydog states, the process is a gently and slow one and do not try to remove too much in the hope of making it perfect - you will more than likely remove too much Nickel. DO NOT use a power tool such as a Dremel or polishing wheel - you will burn through the Nickel as it is thin. Not trying to be a hypocrite here, but I do sometimes use a Foredom Electric mototool on certain parts as I do have extensive experience (50 years) with one. Unless you are very experienced with one, do this by hand. It will take a little longer, but you lessen the potential for damage quite a bit.
NOTE: On small parts such as screws, Cylinder release thumb piece, Cylinder, etc. where Nickel is missing and chipped off, this little trick I use works very well if no replacement parts are on hand. Simply and lightly polish the area where the Nickel is chipped (usually black in color) and polish with Flitz. Basically, you are brightening up the raw steel to make it look like it is Nickeled. You also need to feather the edges so a smooth transition from plated to non plated areas feel and appear smooth. This is the time to repair any screw heads that are buggered, (prior to polishing). There are times I do use my Foredom Electric Moto Tool with a felt wheel and Flitz at a very slow speed so no Nickel is "burned off". Also, I have 50 years of experience with these Moto Tools and while I do sometimes use it, I do know how to do so . Many novices will do more harm than good with a power tool - just fair warning!
While a chipped, stained or worn through Nickeled finish will never look brand new again, I can usually get them looking so good most guys will never know Nickel chipping has occurred. Resist the urge for perfection here as there is only so much Nickel to work with!!
As usual, when reassembling is done, clean Flitz off of all parts and
lightly lubricate. IMHO, polishing a guns Nickel finish should only be done
once, not on any regular basis!
. Never had one with this finish. Dont mean to sound stupid! Its like making love to a foreign girl.
