The main flaw of Oedipus was his pride, or what the Greeks called hubris. This was an important concept to the Greek and it went counter to their whole society. Let me explain this point a little by looking at the oracle of Delphi.
The Greeks believed that the oracle of Delphi was the belly button of the world. And at Delphi, there was two important slogans. The first one was, "nothing in excess." The second one was, "know yourself." If we think about these two things, they speak of boundaries to a certain degree. If you don't do anything in excess, then you are keeping within boundaries. And if you know yourself, then you will know that you are a mortal and not a god!
From this angle, we can say Oedipus broke boundaries. He thought he could solve any problem, such as the plague. He thought that he could outwit the gods. If you read the play, he drives the action completely. He leads to the investigation. He leads to his demise. Yet, on the other hand, this is tragic, because he is also so able. This is the Greek tension.
Hubris. Hubris is the ancient Greek term for excessive pride. In many anceient Greek tragedies, hubris was the hero's tragic flaw. Hubris was a commonly used tragic flaw that encompasses many ideas. Hubris was often used by the ancient Greek playwrights to illustrate what happens to a person who thinks he can defy the gods.
In the case of Oedipus, good old Ed tried to outsmart the gods (hubris) by attempting to escape his fate. His parents were also guilty of this crime, which is why his father ends up dead and his mother end up doing so many messed up things she kills herself. An oracle gives the prophecy to Oedipus and his parents. Supposedly the gods spoke through oracles, so to try to defy the prophecy of an oracle was to defy a prophecy of the gods. To defy the gods was to commit hubris.