I had to go and pick up the quests for the Flashpoints first then log out and back in to queue for flashpoints.
That's weird. I have never picked up the quests and had no problem from level one to 29 or so getting FPs at every level. At the same time someone else at the same level couldn't get into say hammer station, I could.
Something is definitely weird. Is it possible you have an instance spawned on one of the FPs that is uncompleted?