"Taken aback" is more a momentary thing, where for an instant one's brain seems to stop because the situation is so unexpected (like getting a spinal injection without prior warning!).
Being "flabbergasted" is usually longer in duration. The person is first taken aback, but the strangeness seems so big and spread-out that they can't "regain their balance" for awhile. Everything seems to be "at sixes and sevens", and they can't make sense of anything (such as why they're getting a spinal injection without prior warning!).
["Taken aback" is a term from the days of sail, when the wind might completely shift to blow from the front for a moment, which would cause the sails to fill the wrong way and the ship to be "taken aback", i.e. stopped abruptly, with an effect similar to a small earthquake.]