Vinegar bath is a good choice for de-rusting... just check frequently (every 30 minutes or so). I scrub under cold running water, and if any rust remains, then return for more soaking.
The BKF does help when washing off the lye and neutralizing. I use it sparingly, and only after lye bath on unplated iron surfaces. It helps to break up superficial rust and gunk. My Wagner skillets tend to develop light spots from the BKF, so I don't let it sit on the surface very long.
I use only Stainless Steel scrubbies for my wash downs, and 'running' water at all times. The only time I use hot water is for scrub down after lye bath. After that, COLD running water only.
BKF should work well for maintaining intact chrome surface.... But would not be good on seasoned iron surfaces, IMO.
It is difficult to find chrome plated pieces in excellent condition, and I usually avoid plated pieces.
Keep us posted on your progress! :)