There is nothing to my knowledge that prevents you from recording the conversation. It is unfortunate that you feel you would have to resort to this action to protect yourself. If you choose this course of action I would encourage you not to flaunt the recording of the session. If there is something in the recording that is inappropriate or illegal I would encourage you to take the recording to your local JAG to ensure any actions you take are not illegal and will not get you in trouble. The JAG could assist you in coming up with a plan to address the issue in a professional manner with your chain of command.
I am sure that senior leaders in the unit will not support leaders being abusive or degrading and would want to take appropriate action to correct the issue and prevent it from happening in the future.
In summary I want to say that recording a leader is a serious breach of trust. Maybe given the specifics of a situation it is appropriate but you must also understand that by recording a conversation and then using it a against an individual will more than likely change your relationship with other members of the chain of command.