Oedipus' flaw is his quickness to anger and aggressiveness. He easily gets into fights over minor issues. His parents were told a prophecy when Oedipus was a baby that he would kill Laius and marry Jocasta so they abandoned him to avoid this fate.
Oedipus is rescued and raised by the king and queen of Corinth. Later in his life, he unknowingly kills his real father at a crossroads because of his quick anger, and then becomes king of Thebes, replacing his father and marrying the queen of Thebes, his mother. He suspects that the king and queen of Corinth are not his parents, and vies to find out who his real parents are.
At the time, Thebes is experiencing horrible plagues, and as king, Oedipus wants to get rid of them for his people. He learns that the only way he can do this is by finding out who killed Laius and serving them justice. He researches Laius' murder, acquires evidence from witnesses, and learns about the prophecy, and all of the information points to him being the murderer, so he tries to find out more in case there is evidence that says otherwise. At the same time, he gains clues as to who his real parents are.
"If you’ll not talk to gratify me, you will talk with pain to urge you."
Oedipus discovers that his real parents are Laius and Jocasta, and he realizes that it was him who killed Laius. Jocasta also realizes this, and is shaken that she married her son.
"I who first saw the light bred of a match accursed and accursed in my living with them I lived with, cursed in my killing"
Jocasta kills herself after realizing that the prophecy came true and Oedipus is incredibly angry and sad. He takes the brooches from Jocasta's dress and uses them to stab his eyeballs and make him blind. Oedipus brought tragedy to himself and his family because of his fatal flaw.
"Darkness! Horror of darkness enfolding, resistless unspeakable visitant sped by an ill wind in haste!"
Oedipus leaves Thebes and exiles himself to Mt. Cithaeron. He leaves his children and his position as king behind, however all of this could have been avoided had he not been rescued from abandonment as a baby.