No, it doesn't. Military personnel, in their capacity as military personnel--and in that video Kelly states he is a military officer--you cannot just say whatever you want. For example, you can't go to a protest, any protest, in uniform because it could be construed you are representing the military.
Kelly as a Senator can say what he did. Kelly as a civilian can say what he did. Kelly as a retired, commissioned, officer and using that position as part of his statement cannot say whatever he wants.
You have no clue.
This changes if you are retired enlisted over 65 and no longer subject to recall or military service, involuntarily retired as a commissioned officer (at the convenience of the government) and no longer subject to recall, or discharged enlisted who have completed their contract with the military. In those cases, you are no longer subject to anything to do with the military.