I know there wouldn't be a problem with grilling in a contained device-- but I don't think you'd be very popular if you set up a charcoal fire on the salt surface. Lots of folks cook out on the salt -- many pits have food.
If you're talking about cooking/having fires on the ground at your campsite -- no holds barred there, although again I expect the BLM would rather you have a fire circle or fire pit if you're not using a gas or charcoal grill. We use both a charcoal grill (55-gallon drum-sized) and a couple or three of propane grills for Salt Talks, and that's fine -- but again, it's not on the surface per se. Notice I said your "campsite" -- there's no camping allowed on the Salt itself, but at Bend in the Road and many other areas adjacent to the Salt -- it's okay.