I can't imagine there being any restriction on the use of MC within walls, but outsied the walls there might be some issues.
Within the kitchen itself, there are sanitary, moisture, and chemical concerns. A commercial kitchen almost has to be treated as a 'wet' location, and the common aluminum jacket won't survive many wash-downs with a lye-based cleaner.
Nor can you run it up inside the duct to power the exhaust hood fan- even though the fans are ordinarily powered that way in other applications.
You need to know more than just the NEC. Look to your health code and fire code for some guidance.