Hi Jose,
I am neither a NASA employee nor have I been a flight controller, but I do currently work in the space business and talked about the job with a then flight controller a couple of years ago. The flight controller work force really contracted with the end of the Shuttle program and cancellation of Constellation. That is indicative of NASA Johnson Space Center in general; at the time I had the conversation jobs at any part of the center were hard to come by. The International Space Station program is alive and well and requires flight controllers, but I believe those positions were absorbed by the Shuttle controllers. All that being said, here are the bits I took away about the job:
1. You need an educational background in science, engineering, or math (STEM).
2. There are two typical paths to a NASA civil servant job (where you are directly employed by the government). The first path is you get involved in internships at NASA while you are student at university and then become a full time employee after you graduate. The second path is you work as an employee for a company that provides engineering support to NASA on a contract basis. In general contractors perform the same work as NASA employees - their badge is just a different color. They are also subject to the funding whims of Congress and do not have the job security of civil servants. However, if you do good work as a contractor you can be in a prime spot to snatch a civil servant job when it becomes available.
3. The International Space Station is a 24/7/365 operation. That means shift work at odd hours, weekends, holidays, etc.
4. You would start out working in a back room supporting the controller on the floor. If that went well, you move on to be the actual controller and proceed to more responsibility. Some controllers move on to be flight directors, who are the individuals that manage the entire flight control team.
5. I believe most people eventually move on to other positions in the Mission Operations Directorate over their careers. I think it is unlikely that anyone has a 30 year career strictly as a flight controller.
If you were interested in this kind of work, in the current environment I would consider seeking an operations position at a new space company such as SpaceX or Blue Origin. Being a flight controller for a launch vehicle would be more dynamic and interesting than space station work, IMO.
If you want to read about mission control in the "good old days" I recommend the following:
1. Failure is Not an Option by Gene Kranz - a book covering Gene Kranz's experiences as a flight director during the Mercury, Gemini, and Apollo programs.
2. Wayne Hale's blog - an internet blog that includes some recounting of Space Shuttle mission control stories.