I'm not sure that Shakespeare was terribly concerned about following classic rules of drama, such as those proposed by Aristotle. For example, Shakespeare violated the rule about unity of place recklessly. In King Lear he has characters scattered all over the map, with various kinds of action taking place. It is as if he is taking a malicious pleasure in violating the rules the French followed so slavishly. I don't believe that Shakespeare was concerned about giving his heroes "tragic flaws." If he handed out a tragic flaw to Caesar, Cassius, Antony, Octavius, and Brutus, it would seem artificial. He was more concerned to humanize these characters, to make them seem like people his audience would recognize. As for Brutus, he was an honorable man who had the best interests of the Roman nation and its people at heart. But he was egotistical, unworldly, bookish, introverted. The worldly-wise Cassius and Antony took advantage of him. Brutus overrated his own intellect. He was overly proud of his ancestry. Once Caesar had been assassinated, Brutus began to think of himself as Caesar's natural successor. He wouldn't listen to advice. He was trying to be a Caesar without Caesar's practical wisdom. Brutus had more than one character flaw, but not necessarily any special tragic flaw. He was human, like all of us.