If you are "Generically" talking about "The Academies"; then either way you wrote is fine. If you SPECIFICALLY want to mention air force or Army, then you should mention them specifically. E.g. "The United States Air Force Academy" or "The United States Military Academy at West Point". Especially if you want the MOC to nominate you for that SPECIFIC academy. But if you are mentioning the academies generically, or you don't care what you're nominated for; then what you wrote is fine, either way.
Most of the essays you do for Academies or nomination applications have word or space limits. It is usually best to be brief and use as much shorthand as possible. The reader will understand the context, and knows what you are referring to if you say "academies". I know my son did essays for USMA, USNA, and USAFA, along with three MOC applications, and with each essay he asked me to help him rephrase parts so they would use less characters. It was a challenge usually to maintain substance and style, but with less words. Acronyms are a way to do that when possible.