One could argue that Jack has two external conflicts. The first is his struggle for leadership of the boys on the island. It is apparent from the very beginning that he has a desire to be in charge. He clearly thrives on the power he has over his choir as evidenced by the fact that he had them marching in their hot robes in an orderly fashion along the beach. He is disappointed when Ralph is chosen but quickly starts building his own faction of hunters.
This conflict slowly builds until he and Ralph have to face off and Jack takes control of the boys and it becomes obvious that Ralph has lost any chance of keeping the boys in order. Once he gains control, Jack quickly evolves into even more of a tyrant, ruling through fear and physical force.
The second external conflict runs concurrent to the first and though it may seem trivial, mirrors the first one in many ways. Jack, at first, is not actually capable of killing and he struggles to track and then even stab the pigs. Obviously part of this conflict is internal but the external side of it clearly ties into his struggle with Jack for leadership.