Can I mount an electrical box on a non-stationary surface?
Absolutely, we use flexible conduit all the time. If flex conduit is installed for flexibility it is limited to 6’ in length. I would suggest stranded conductors for longer life but code is not specific on that. metal flex is handy and industrial plants do just what you want to do routinely it is code compliant so FMT or flexible metal tubing (usually just called metal flex).