The boards are made up of civilians, so generally speaking, they are not bound by the UCMJ (there is a somewhat "theoretical" exception for those civilians who are retired military).
The recourse is in Federal Court. For disability claims, most likely would be US Court of Federal Claims. The problem with military awards is that, though they can represent enormous pride and can impact certain other benefits, there is no monetary value to them by themselves. This makes pursuing an appeal to a denial more difficult for a number of reasons.
In cases like that (and in most BCMR/PDBR, for that matter), it makes more sense, in my opinion, to seek legal representation when you first file to the administrative board. The reason for this is that you can get a good assessment of your case, maximize your chances for success at the board, and very importantly, will have raised issues that a reviewing court will find compelling. Remember, failure to raise an issue at the administrative appeal level often means you cannot raise it later for the first time in court.