How does Shakespeare use the concept of revenge with Macduff throughout the story?
Macduff is the hero of the play Macbeth. More, he is a nemesis and foil to the villain Macbeth. Specific to your question, he is both a revenger and avenger in the play. His primary goal is to kill the villain Macbeth. His secondary goal is to restore order to Scotland.
As an avenger and a loyal Thane of Scotland, Macduff must kill Macbeth, regardless if Macbeth has killed Duncan or Macduff's family or not. A Thane's duty is clear: all traitors must be executed. Macbeth did the same in Act I when he killed Macdonwald. This helps to maintain Comitatus and the social order.
As a revenger, Macduff must kill Macbeth for the crimes of killing Duncan and his family. This is more personal. Malcolm urges Macduff to kill Macbeth as an act of revenge:
But Macduff partly blames himself for his family's murders. He says:
Later, after he properly grieves his family, he will make the revenge more personal:
Macduff is not a monologuer, the kind you see in action movies who make a long speech before they kill; instead, he speaks with steel. After all, speaking is not an act of revenge.
It is important to note that Macduff's revenge is targeted and controlled. It is of the "eye for an eye" variety, not a gratuitious, overly passionate affair where one kills for the sake of killing. So says Enotes editors:
In this natural frame of action, Macduff is able to move toward the final confrontation with Macbeth in a deliberate and highly focused manner, refusing to strike down the reluctant soldiers in Macbeth's force and seeking his revenge on Macbeth alone.
Shakespeare doesn't necessarily use Macduff throughout the entire plot of his Macbeth to further the idea of revenge. Malcolm and Donaldbain are first to have a concrete reason for revenge when their father the king is killed.
Macduff enters the realm of revenge-taking when he is the one who questions Macbeth about why Macbeth kills the grooms, who could have served as witnesses (Act 2.4). This plants the seed for later events that actually lead to Macduff achieving revenge. His questioning Macbeth suggests that, since Macbeth kills the grooms, Macduff suspects him of treachery.
Macduff's need to get revenge apparently grows as the play progresses. He goes to England to join with Malcolm against Macbeth. Then, when he gets the news that Macbeth has had his family killed, the revenge becomes personal.
Macduff, then, begins to question Macbeth after Macbeth kills the grooms, decides that Macbeth is, indeed, guilty of treachery as the play runs its course, then receives the news that his family has been killed and his revenge becomes personal.