Or the Key Flaw can be seen as sarcasm, and the fear would be the reason for it. One cannot approach this in an overly regimented manner. Usually, though, one takes precedence. So in the case being discussed, the two are so closely related that, yes, there can be two. Very frequently, a fear is associated with the Inner Need.
Many stories have an outer and an inner track.
Thus, the external story is about the events and efforts to achieve the goal, despite difficulties. There may be other internal conflicts as well, such as when values clash, or when a character must choose between two almost equally desirable things, or between two bad options. A story that has only the outer track usually seems too empty, too superficial, too thin. It's generally unsatisfying. The inner track adds resonance, significance, and power.