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.
BioWare announced 3 difficulty levels for Operations: Normal, Hard, Nightmare.
I also vaguely remember they announced the same 3 difficulty levels for flashpoints too (There were definitely 2), but maybe that was just wishful thinking and perhaps the 3rd "Nightmare" mode was only for operations.
But isn't there a way to set a given operation or Flashpoint from Normal to Heroic?
I was under the impression that that was the OP's question.
I don't know for sure, but if I were to take a wild guess, I would expect the group leader to have a "difficulty mode" setting in their right-click menu when they click on their portrait ... But the reason I expect that is because I've played WoW for too long :P
But in any case, the right-click portrait menu seemed fairly familiar to me from WoW when I tried Black Talon in beta (around L11-L12, I wasn't the party leader, just a groupie). There were all kinds of options such as "leave party" and marking mobs and players with icons like a yellow star.. Very familiar :P