Both stories obviously represent the dark side of ambition. In Lord of the Flies, Jack's reaction to finding out that there can be rules and he can enforce them with punishments demonstrates that he just wants power.
“We’ll have rules!” he cried excitedly. “Lots of rules! Then when anyone breaks ’em–” (ch 2)
Jack fights Ralph for power in a more direct way than Macbeth fights Duncan, but the result is the same in that Jack creates his own little kingdom out of the choirboys. Malcolm creates an army from his supporters that flee because of Macbeth.
Macbeth does not want to be king at first. When the witches tell him he will be Thane of Cawdor and then king, he seems to think this will be real.
The Prince of Cumberland! That is a step(55)
On which I must fall down, or else o'erleap,
For in my way it lies. (Act 1, scene 5, p. 18)
Nevertheless, Macbeth does wan t to be king. He decides that if he is not named king, he needs to take the throne himself. When Jack is not chosen leader, he too decides to make himself leader.
Macbeth, like Jack and his gang of boys from Lord of the Flies, reverts back to a more violent, primitive way of life. In order to ensure their safety, both Macbeth and Jack wield power ruthlessly. If you are not with them, you are in danger of losing your life.
Both the "Lord of the Flies" as well as "Macbeth" have a similar theme - that ultimate power corrupts absolutely.
In Golding's novel, the boys, who are innocent upon their arrival on the island, become evil because there is no one there to stop them. Jack and his gang soon learn this and use fear and terror to control the others.
Shakespeare also depicts an innocent and brave soldier in Macbeth at the beginning of the play. However,his ambition gets the best of him and he becomes a tyrannical leader.
Both texts also rely heavily upon pathetic fallacy as a technique to highlight the characters' inner turmoil or savagery. Pathetic fallacy is when events in nature mirror the characters' inner conflicts. For example, when Macbeth is about the Kill King Duncan, there are all kinds of strange occurrences in nature. (there's thunder, lightning, horses eat each other... ) In "The Lord of the Flies" there's a violent storm out when the boys "accidentally" kill Simon on the beach (during one of their primal ritual dances).
I hope that this helps.
I think you could make an argument for similarities in the darkness of man's heart and man's natural want for leadership also. In both LOTF and MB, we see characters who hunt/kill in order to gain leadership and prestige. In both we also see characters who should morally know better than to hurt friends but can't seem to help themselves from doing so.
It could possibly be seen that once an act of savagery is committed it unleashes a drive to fulfill the dark side of human behavior. In Macbeth, once he had killed Duncan, he felt the need to kill any threat-no matter how insignificant(think Macduff's family).
In LOTF, once the boys had a taste of bloodlust, they pushed the boundaries further until hunting pigs was not enough to satisfy them.