Okay. What possibilities exist for the military? You have a thing, an mRNA vaccine that the military developed as a weapon. First and foremost, it's neither cheap, nor easy to develop. Further, it's not easy to deliver. The enemy will need to have been inoculated with a vaccine that degrades very quickly and requires special measures to preserve and finally, it's very, very difficult and expensive to develop an mRNA vaccine, especially one that doesn't immediately get neutralized by immune cells.
All for what? The ability to stimulate the synthesis of particular proteins? What possible outcome would the military hope for? There are a host of other biological agents that could be used if there weren't treaties in place that would preclude the US military from legally doing so.
Like most conspiracy theories, this doesn't pass the Occam's Razor test.