What was Oedipus's tragic flaw?

For many years there's been a fairly intense debate raging in academia as to precisely what constitutes Oedipus's tragic flaw. It's not possible to provide a definitive answer to the question here, but there are a couple of possibilities that we can examine.
The first of these is pride, or hubris, as the Greeks called it. When Oedipus visits the Oracle at Delphi, she tells him that one day he will kill his father and marry his mother. Understandably, Oedipus is shocked at hearing this, as anyone would be. Less understandably, however, he chooses to defy fate, displaying extraordinary hubris in the process. Ironically, his act of overweening pride ultimately leads to his downfall. It's precisely because Oedipus refuses to return to Corinth that he ends up meeting his birth father, Laius, on the road, where he subsequently kills him.
A slightly less convincing case could be made for anger as Oedipus's tragic flaw. After all, it's anger that leads Oedipus to kill his father. There are two problems with this approach, however. First of all, although anger does indeed lead directly to Laius's death, it has nothing whatsoever to do with the other part of the Oracle's prophecy: that Oedipus will marry his mother. In fact, this has more to do with the hubris that Oedipus displayed in solving the riddle of the Sphinx, for which he was rewarded with Jocasta's hand in marriage.
The second problem with the anger case is that Oedipus's killing of Laius could reasonably be justified on the grounds of self-defense. Certainly, most of the audience watching Oedipus Rex will have arrived at the same conclusion. After all, Oedipus, like Laius himself, is a king, and as such would be expected to defend his honor, by force if necessary.
On balance, then, hubris would seem to be the most likely answer to your question. However, the matter is far from settled. The important thing is to read the play carefully and make up your own mind.