Does having two masters degrees give you a better chance when applying for Naval OCS or Air Force OTS?

a lot depends on how well you do on their officer qualification test.

It is a factor but not a deciding factor. They still look at whole person concept. I have seen many an aerospace engineer not get picked up. They know how to design the plane but some just don't have the aptitude to fly it. Different skill sets. Yes it will look good and may give yo a slight edge but won't be the initial deciding factor. IMHO.

Seeing the comments below, I'll offer the other side of the two edged sword. Multiple degrees can also be and indicator that the person is best qualified to be a professional student. And, what does that get you? Multiples of one single pedigree item doesn't mean much more positive, but can drift the other way. I saw that in some of the officer candidates I used to screen for the Accessions Program. Some of them still didn't know what they wanted to do when they grew up. Others thought doubling or tripling down meant two or three times credit. Still others thought the degrees yelled how rounded they were when in fact, during the interview process, it showed how lost they were.

Bottom line, there's some sage advice from folk that know more than I about the things you must do. The closest I came to your track was being a friend of Dave Brown, Flight Surgeon. Up on Adak as a LT, he said he was going to be an Astronaut. We all believed him. He wasn't snotty about it. Just quietly pursued his dream daily. It just was his ever present and focused goal. He succeeded. Unfortunately we lost him on the Columbia. Yeah, quite a different breed.