In Macbeth, why do Duncan's sons flee, and how does this help Macbeth?
Concerning Shakespeare's Macbeth, Malcolm and Donalbain flee after their father's assassination because they fear for their lives. As Donalbain tells his brother: "Where we are / There's daggers in men's smiles" (Act 2.3.140-41). Whoever killed their father is still in the castle, and they are obviously targets: "The near in blood, / The nearer bloody," concludes Donalbain. In other words, the closer their relationship with Duncan, the more likely they are to be murdered, and just because the thanes act sad that Duncan is dead and act like they are loyal to the brothers, any one of them could be lying and pretending.
Remember that Malcolm has just recently been designated as Duncan's heir by Duncan, and also that Duncan warned Malcolm that you cannot tell what a person is thinking by looking at his/er face. The brothers are prime targets, and they know it. Thus, they flee.
This, unfortunately, casts suspicion on them, and makes it less likely that anyone would assume Macbeth is guilty. Other characters assume that the brothers assassinated their father, and that they flee in order to escape prosecution, all but Macduff, anyway.
Ironically, Macbeth might have gotten away with the assassination, except that he varies from his wife's plan and kills Duncan's grooms. This makes Macduff suspicious, and leads to rebellion.
Following their father's assassination, Malcolm and Donalbain flee from Scotland because they fear for their lives. In act 3, scene 2, the siblings learn about their father's death and become suspicious that the murderer is still alive and undiscovered. After Macbeth admits to killing Duncan's chamberlains out of anger, Donaldbain suggests to his brother that they leave the castle immediately. Donaldbain tells Malcolm,
"What should be spoken here, where our fate, Hid in an auger-hole, may rush and seize us? Let’s away. Our tears are not yet brewed." (3.2.102-104)
After everyone exits the scene, Malcolm tells Donaldbain that any of the lords could be pretending to be sad and upset, which is why he is leaving for England. Donaldbain agrees that they will be safer in other countries and tells his brother that he will be traveling to Ireland. Both siblings then leave Scotland to ensure their safety.
While Malcolm and Donaldbain save their lives by fleeing the country, they simultaneously incriminate themselves by doing so. Many of the Scottish lords believe Duncan's sons participated in their father's assassination, which explains why they fled the country. Being that Macbeth is a high-ranking thane and Duncan's cousin, he becomes Duncan's successor and is given the title King of Scotland.