Virginia State Police said the suspect's vehicle had been spotted on the Interstate 66 highway following the shooting, and crashed off the road after being pursued by officers.
"Troopers approached the vehicle and found the male driver suffering from a self-inflicted gunshot wound," the force said in a statement.
He later died in hospital, a police spokesman said.
The Twitter account of Flanagan suggested he had held a grudge against Mr Ward, 27, and Ms Parker, 24.
Police said his utterances on social media the previous evening suggested the attack was pre-planned.
ABC News has meanwhile revealed that it received a 23-page fax, apparently sent by Flanagan on Wednesday morning, in which he claimed his anger had been "building steadily".
The fax said the attack was intended to avenge the Charleston shootings earlier this year - a suspected hate crime in which a white gunman killed nine parishioners at an African-American church.