Yes, Fleance, the son of Banquo is able to flee to safety, thereby fulfilling the prophecy of the three witches and spoiling Macbeth's plan. But if you recall in Act I, scene iii, when the witches "hail Macbeth that shalt be King hereafter," Banquo asks them
If you can look into the seeds of time
And say which will grow and which will not,
Speak then to me, who neither beg nor fear
Their response is that he will be
Lesser than Macbeth, and greater.
Not so happy, yet much happier.
Thou shalt get kings, though thou be none.
These are the prophecies, or fates if you will , of Macbeth and Banquo, so you see Macbeth's plan fails because it is fate. Yes, Macbeth attempts to alter fate, and finds out that he cannot.
The Weird Sisters tell Macbeth at the beginning of the play that he will be king, but they also tell Banquo that he is "lesser than Macbeth, but greater" and that his children will someday be kings. Since the prophecy comes true for Macbeth, he needs to come up with a plan for stopping the other part of the prophecy, that Banquo's heirs will be the future kings of Scotland. Even though they are good friends, Macbeth hires murderers to kill his friend and his son, Fleance. The murderers come upon the father and son, easily killing Banquo. Fleance, however, is able to escape. When Macbeth is told that the boy was able to run away, he fears that the Weird Sisters' prophecy will yet again come true.
Macbeth's plan to defy the witches' prophecy fails because Fleance gets away and only Banquo is killed.
The witches had predicted that Macbeth would become Thane of Cawdor. And they had predicted that Macbeth would become king. Both of those happened. But now Macbeth is worried because the witches also said Banquo would be the father of kings. Macbeth wants his own sons to be kings after him and he doesn't want Banquo getting any ideas about killing him the way Macbeth killed Duncan.
So Macbeth wants to have Banquo and his only son killed. He tries, but Fleance gets away.