...learn all the key words and tricky phrases....
Good thing to mention. You could have the knowledge to physically build your own reactor, but that doesn't mean much for the tests. Not only do you have to know the material, you have to know the material for the tests word for word, from the book the Navy gives you, and it's not a multiple choice test/fill in the blank but pretty much essay type answers for every question. Your chem-e degree may help you grasp the concepts easier which will free up gray matter for the tests, but the answers are no less easy if you can't remember, as Steve said, the "key words and tricky phrases".
As an easy example, a monkey wrench in Nuke parlance is an "open-end adjustable pipe wrench". Miss any of those words and you just missed the question. Doesn't matter if you can describe the material it made out of, it's molecular structure, it's color, how much it weighs, what it does, , etc, etc, you leave out any of those words...no dice.
Good luck, nuke school is a challenge but it's rewarding too.