I supose this is going by Final Fantasy III and onwards, if we base it on the six classes from FFI(and upgrades), it would end up like this:
 
Twilight-Black Mage, powerful Magic.(though overall, she should be a sage, suposelly master of all magic)
 
Rainbow Dash-Warrior/Fighter, a physical attacker for sure, and as Fighter becomes Knight, it fits her element.
 
AJ-Monk, again, a physical attacker, even stronger that the Fighter, the discipline of a monk could be related to her taking family as priority.
 
Pinkie-Thief, agile, becoming a Ninja would be perfect for Pinkie if we don’t need stealth.
 
Fluttershy-White Mage, always caring for the others, her greatest wish would be that no one ever gets hurt in battle.
 
Rarity-Red Mage, stylish, decent magic user, decent physical battler(remember, Rarity knows Kung Fu!), though will never be as good as the Black Mage or the Fighter/Monk on those aspects.

Pinkie should be a bard and Fluttershy should be a ranger

I think fluttershy would be more of a white mage instead of a dragoon. o_O

What about the thief and white mage?