In order to fly in the United States, you will need to present a valid form of government-issued identification, such as a driver's license or passport. If your name and date of birth match those listed on the warrant, the airline may be required to notify law enforcement and prevent you from boarding the plane.
Additionally, if the warrant is for a serious offense, such as a felony, law enforcement may be able to track your movements through electronic means, such as cell phone signals or credit card transactions. In such cases, you may be apprehended at the airport or during your flight.