What does the ending of 2015's Macbeth mean?

The ending is not based on actual history since the history of Banquo and Fleance are dubious at best.

Although Macbeth was a historical figure, the characters of Banquo and Fleance are questionable. Shakespeare used the works of Raphael Holinshed when writing historical plays. Banquo is mentioned by Holinshed as an accomplice of Macbeth in his usurpation and as being the ancestor of the FitzAlan High Stewards of Scotland, from whom King James I descended. Holinshed's chronicles were disproven when historians discovered that the FitzAlan family descended from a Breton family. There did exist a historical figure called Banquo Thane of Lochaber, however there is no historical evidence supporting that this individual was a descendant or ancestor of any Scottish rulers.

The significance of Fleance taking Macbeth's sword suggests that Fleance is wishing to fulfill the prophecy as shown by the three witches. The witches prophesied that the descendants of Banquo shall be kings. Fleance is shown taking the sword of Macbeth to symbolize how strongly he feels about the prophecy being realized and that he will take the throne by force if necessary. It is really meant to be an ambiguous use of symbolism.

There is really no need for Malcolm to actually chase after Fleance. Malcolm's claim to the throne is evident. It is interesting how the filmmakers chose to have Malcolm simply looking upon his sword and crown rather than actually taking possession of them. This is also meant to be an ambiguous use of symbolism. The viewers are left to question if the prophecy of the three witches is to be fulfilled or if Malcolm will actually occupy the throne.

In actuality, Macbeth was succeeded by his stepson, Lulach. Lulach had a short and unsuccessful reign and was then succeeded by Malcolm III.

Perhaps it is a ominous suggestion foreshadowing that Fleance may choose to fulfil the witches' prophecy in the same way that Macbeth did: by force. Seeing as Shakespeare wrote this play with King James I in mind, and King James had a known hatred of witches, he would have most likely wanted to suggest to his audience that the witches were the cause of the whole tragedy. The director of this Macbeth may have picked up on that, and left the ending open to the idea that the witches' prophecy creates an endless cycle in the struggle for the throne, fuelled by the desire to fulfil a fate told by the witches.

By having Fleance's scene parallel to Malcolm's, it might suggest that those rightful to the throne will receive it, whilst those who choose to seize it upon prophecies told by witches, like Macbeth, will fail,and end up a tragic hero.

I'd argue that thematically, it's the same. Staring at his sword, from the throne, in contemplation, he walks out towards the light. That's a classic way of showing that he's going towards a better future, that there is work to do. The child, aka the future, taking Macbeth sword and walking towards the light from the fog, means the same, towards a better future.

Only difference being that movies are primarily Show, vs a book or plays Tell.

This particular adaptation of Macbeth focuses less on ambition and greed as motivations for the murder of Duncan and rather examines PTSD and the death of the Macbeth's baby as triggers. The last scene is meant to show (I think) how, because of the scenes of violence Fleance has experienced as a child (his dad being murdered in front of him, as well as Macbeth), he is destined to follow a similar trajectory to Macbeth i.e. kill the current King.

Um - I thought the film ending was pretty obviously foreshadowed by King Macbeth’s decision to believe the prophecy about Banquo: he tries to murder both father and son, and Fleance escapes.

The final scene is precisely the same, only a different king ;-)

In the play, Banquo is no part of Malcolm’s family: in the last scene Malcolm realizes and Fleance remembers what the prophecy means.

So Malcolm sets off to finish the job Macbeth began, and Fleance once again begins to run for his life.