Flagg, who plays shooting guard or small forward, helped Duke University reach the National Collegiate Athletic Association (NCAA) Final Four in 2024-25, averaging 19.2 points, 7.5 rebounds, 4.2 assists, 1.4 steals and 1.4 blocks per game as a freshman.
He won the Wooden Award – given to the most outstanding college player each season – and was named Atlantic Coast Conference Rookie of the Year.
He is the second number one overall pick in Dallas franchise history after the Mavs selected Mark Aguirre in 1981.
The San Antonio Spurs took guard Dylan Harper with the second pick.
Harper, 19, is the son of five-time NBA champion Ron Harper and his older brother Ron Harper Jr on the books with the Detroit Pistons.
“I’m feeling everything – all the emotions mixed in one bucket,” Dylan Harper said.
“They’ve got a great young core over there. I’m just ready to get in there and make an impact any way I can with those guys.”
Guard VJ Edgecombe was selected third by the Philadelphia 76ers.
Born in the Bahamas, he was named Big 12 Freshman of the Year after averaging 15 points and 5.6 rebounds per game at Baylor University.
The Charlotte Hornets used the fourth pick to bring in guard Kon Knueppel.