Well, you can only have one base profession, but you aren't limited in the number of elite professions you can own.
If you have more than two professions, you may only advance two of them at a time (the two you decide to advance can both be elite professions, if you wish). You are, effectively, "giving up" a profession (although you retain all of the skills and abilities you have earned) while you focus on your other career path. 
Taking your character as an example:
She uses the Starship Duty professional ability to acquire the Starship Command Officer elite profession (since Starship Duty allows you to forgo the other requirements of a starship officer elite profession), and spends the remaining two picks on Starship Command Officer skills to fulfill her requirement for spending 1 advancement on the profession.
At that point, she must decide which profession she leaves behind (flight control or starship officer) to pursue her command career. If she leaves the Starship Officer profession, then she would have to spend one full advancement to return to it later on in her career.
For another example, I have an NPC character that I based on one I played in a free-form PBEM game. He started out as a Starship Officer and Starship Engineer...about four advancements in, he dropped Engineer to become a Starship Security Officer (using Starship Duty). He was a Security Officer for about a dozen advancements before becoming the XO of a ship and taking the Starship Command Officer profession (again using Starship Duty), and dropping Security Officer.
A disastrous event eventually led to his dismissal from Starfleet, where to he spent the next two advancements to return to his security and engineering professions to become a security systems design specialist for ASDB.
Now, he took a convoluted path, but it serves as an example of how you would manage multiple professions over a career.
Page 155 of the PG does a good job of explaining the process in the two examples on Mr. Sechok.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz