Forgive my lack of military understanding, but shouldn't a Flag ship have a flag officer on board? The Enterprise is often described as the Flag ship, but which flag officer does this refer to, or does it just mean "it's our most famous ship" ?
That's a different meaning of flagship. Dictionary.com defines it as:
1. a ship carrying the flag officer or the commander of a fleet, squadron, or the like, and displaying the officer's flag.
2. the main vessel of a shipping company.
3. any of the best or largest ships or airplanes operated by a passenger line.
4. the best or most important one of a group or system: This store is the flagship of our retail chain.
Here, it is being used in the 4th sense. It is the most advanced, best, prettiest, coolest of all Federation ships. It is, therefore, the federation's flagship. It similar to saying that Windows is Microsoft's flagship product.