How does an early separation for education work for the Navy? When should I put in my special request chit?

I believe the process is similar across branches, but in the Army, you have to show you are enrolled to start at a physical location. The semester has to start within the last 90 days of your contract termination date.

Regardless of what information you get here you will need to speak to your immediate leadership and your base education office. Between those two resources you will be able to start the process because you will need input by both resources.

Your chances depend on a lot of things that may be out of your control, like how your rate is manned at the E3 and E4 levels, and what your LPO and LCPO think of you and if you're using it responsibly. Keep in mind, that an early out just adds the time you would be recallable.