The challenge is to get James III's bloodline back into the current British royal family. In part this was inspired by the fact that William, Duke of Cambridge will be the first monarch to descend from Charles II since 1685, and his son will be the first to descend from Henry VIII since Gloriana died. James is a little bit more tricky. Obviously it's excessively unlikely that it'll be straight-up Stuart/Stewart blood, thanks to the Act of Settlement and all that.
Rule: One of the Jacobite risings cannot result in the Hannovers being overthrown and we get a Stuart king, hence why the challenge is worded 'blood'. Nor can it happen (although this is ASB-sort unlikely) that Bonnie Prince Charlie has a (great-)grandson who marries Princess Charlotte or Victoria.
Hint: Victoria was very fond of her Scottish ancestors, and Princess Olivia of Cumberland and Count Roehanstart might've been onto something
Have at it and good luck