Originally, BRAT is stood for British Regiment Attached Traveler. Basically, the wife or child of a British soldier. These days, military brat (or army brat, navy brat, etc.) refers to children of military families, especially ones who move a lot. - "I've moved three times in the past four years." - "Wow, that's a lot!" - "Yeah, well I'm an army brat, so it can't be helped." You wouldn't really use it to describe non-military families who move a lot. However, if you said might be able to say something like, "I moved around a lot as a kid because of my dad's job. I'm a salaryman brat!" as a joke if the context was right. との事です。
刑事ものや軍事関係の小説や映画に出てきた略語というと、「到着時死亡」とか「作戦中行方不明」とかもあったような気が。DOA とかMIA だったような気がします。death on arrival missing in action だったかな?うろ覚えです。こういう業界用語?みたいのはどこの世界でもたくさんあるんですね。