How old was Fleance when Banquo was killed in Shakespeare's Macbeth?

Fleance was young enough to be called “boy” when Banquo was killed.

Although Fleance’s exact age is not mentioned, Banquo does call him boy.  Macbeth has no qualms about killing him, but that doesn’t mean anything.  He kills Macduff’s wife, son and entire family.  Fleance is a danger to Macbeth because the witches’ prophecies mention Banquo’s sons.

Macbeth seems to be particularly interested in the prophecy about Banquo’s sons, even before he kills Duncan.

MACBETH

Your children shall be kings.

BANQUO

You shall be king. (Act 1, Scene 3)

After killing the king, Macbeth decides that Banquo and Fleance are too dangerous to be left alive.  Banquo is a double threat because he knows about the prophecies and might suspect that Macbeth killed Duncan, and because his sons are supposed to be king.  Fleance, already Banquo’s son, is a threat too because he might someday become the king.  If Macbeth kills them both he eliminates both threats.

The first time Fleance is introduced, Banquo calls him “boy.”

BANQUO

How goes the night, boy?

FLEANCE

The moon is down; I have not heard the clock.

BANQUO

And she goes down at twelve. (Act 2, Scene 1) 

When Macbeth is giving instructions to the murderers, he says that it is important that both Banquo and Fleance be killed.  He does not say how old Fleance is, but he says that his absence “is no less material” that his father’s, so it is possible that he actually is rather young, so that to most people he seems insignificant.  To Macbeth he is important because he might one day be king, so he has to die.