Fleance is Banquo's son, and his escape keeps the prophecy alive: Banquo's descendants will be kings.

He appears with his father at night (Act 2, Scene 1), escapes the murderers (Act 3, Scene 3), and is implied in the show of kings (Act 4, Scene 1).

"Fleance is 'scap'd." (Act 3, Scene 4). Three words from a murderer destroy Macbeth's security. He replies "Then comes my fit again", and his mind breaks at the banquet minutes later.
"Whom, you may say, if't please you, Fleance kill'd, / For Fleance fled." (Act 3, Scene 6). Lennox mocks the official story, showing how absurd Macbeth's version of events has become.

Structurally, Fleance's escape is the first failure of Macbeth's plans. Use him as a symbol of a future that cannot be murdered, and pair him with Macbeth's "fruitless crown" (Act 3, Scene 1). In Holinshed, Fleance's descendants became the Stuart kings, so his escape is also a nod to James I.

Fleance is Banquo's son, and his escape keeps the prophecy alive: Banquo's descendants will be kings.

He appears with his father at night (Act 2, Scene 1), escapes the murderers (Act 3, Scene 3), and is implied in the show of kings (Act 4, Scene 1).

"Fleance is 'scap'd." (Act 3, Scene 4). Three words from a murderer destroy Macbeth's security. He replies "Then comes my fit again", and his mind breaks at the banquet minutes later.
"Whom, you may say, if't please you, Fleance kill'd, / For Fleance fled." (Act 3, Scene 6). Lennox mocks the official story, showing how absurd Macbeth's version of events has become.