I never got the chance to check this out while in Beta. Can anyone shine some light on how you change the difficulty?
This is not a single player game, so you cannot manually change the difficulty.
There are 2 classes of flashpoint (someone correct me if I am wrong there), and 2 classes of Operation: Normal Flashpoints, which are easier than Normal Operations (the "Normals" are the type that you do at "any" level), then Heroic Flashpoints which are harder than Normal Operations but easier than Heroic Operations.
As far as I know, the Heroic versions become available when you hit level 50.