Just to add to what LM stated, your rank in the Navy means nothing once you get hired on. You "may" get hired into a supervisor role, but that is extremely unlikely. Supervisory roles at a utility require experience. Yes you have experience operating the Navy's reactors, but is very different on the outside. Also, ANSI standard 3.1 contains requirements for education and experience for different positions within a Nuclear plant.
One thing to toss out there. As a Chief in the Navy, you are responsible for EVERYTHING, including what your sailors are doing on their own time. Operations, maintenance, cleanliness, training, etc, etc, etc. Out here, you work EITHER operations OR maintenance. Also, unless you end up in a supervisor position, if Little Timmy doesn't show up to work on time or has a DUI, you don't have hours of paperwork and babysitting to do. Even as a supervisor, you pretty much are just keeping management appraised of what is going on. Where your experience as a leader can come into play is once you get into a NLO/Licensed Operator class. Acting as a pseudo role model for those folks that are new to Nuclear. Show them how to apply yourself, help them develop good study habits. Show folks how integrity and strict compliance to standards works.
Start on a resume. Don't attempt to make things sound more important or useful than they are. There's a good chance the manager looking at your resume will have had some Navy Nuke experience and see right through the smoke screens that we try and throw up. Just a little last minute advice.
Good luck and thank you for serving!