Compare and contrast Jesse James, Macbeth, and Hamlet. How did they all lead themselves to their own downfalls? How are they different? What is their tragic character flaw?

The single most obvious feature that would seem to link these three figures is that all of them were "rebels" in some sense. But they were rebels in completely different ways, and we have very little to go on if we're trying to establish similarities or parallels among them beyond this surface factor, either in terms of their personalities or the activities they engaged in that account for their fame as historical figures or as literary characters.
Jesse James has been glorified as a kind of Robin Hood, though if we look at the actual facts rather than the legends that were built around him, it's difficult to see anything positive or admirable. He and his brother Frank were Confederate guerrillas who took part in the irregular, partisan fighting in the border state of Missouri. After the war, they continued fighting through criminal activities because they were among the many who basically refused to accept the outcome of the war and the victory of the Union over the Confederacy. The pro-Southern orientation that dominated much historiography and much of the popular culture as well—even in the North—in the decades after the war, and clear up to the middle of the twentieth century, is responsible for James's being perceived as a heroic figure. In reality, he was a ruthless criminal, and only those with a neo-Confederate perspective today would find anything admirable or positive about him.
Both Macbeth and Hamlet, in Shakespeare's portrayals, defy authority—Macbeth by carrying out murder in order to gain power for himself, and Hamlet by causing havoc at the Danish court to avenge his father's murder at the hands of his father's brother Claudius, who became king. Though Macbeth is a criminal, like Jesse James, he is a man the audience nevertheless instinctively identifies with. He has been victimized in some sense, driven on by prophecies, the urging of his wife, and his own inner demons, and he becomes a symbol of man alone, helpless in the face of a hostile or simply meaningless universe. Hamlet is confronted by a situation in which he has no recourse but to take private revenge and essentially sweep aside anyone who gets in his way, including innocent people like Ophelia and her father, Polonius. The audience sees him, as it does Macbeth, a sympathetic figure, because he, too, is a victim of uncontrollable forces both external and internal.
These factors that cause us to identify with Hamlet and Macbeth, in my view, are absent from Jesse James's history. As we've stated, the only connection between James and Shakespeare's tragic heroes is that of the defiance of authority, but in the end, this is a superficial similarity when we consider the much more significant differences.