He played college football for the North Texas State Eagles and was selected by the Oakland Raiders in the 1960 AFL draft.

[1][3] Although selected in the fifth round (55th overall) of the 1960 NFL draft by the Pittsburgh Steelers, Haynes chose to play for the AFL's Dallas Texans, signing his contract with the team under the goal posts of Kidd Field after the 1959 Sun Bowl.

He was Hall of Fame head coach Hank Stram's most versatile and dangerous weapon from 1960 to 1962, amassing 43 touchdowns and 4,472 yards on rushes and receptions.

In 1962, he helped the Texans win the AFL championship game in the classic double-overtime victory over the two-time defending champion Houston Oilers.

In that game, Haynes scored touchdowns on a 28-yard pass reception from quarterback Len Dawson, and on a 2-yard run.

Haynes believed that the trade was retribution for his participation in several black players boycotting the 1965 American Football League All-Star game, which was supposed to be in New Orleans, due to the black players' mistreatment by hotels and businesses in New Orleans.

Haynes had three games in which he gained 100 or more yards on 14 or fewer carries, and was selected to the All-Time All-AFL second-team.

In 2019, the Professional Football Researchers Association named Haynes to the PFRA Hall of Very Good Class of 2019.

[13] Coach Stram, aware of the strong winds at Jeppesen Stadium, instructed Haynes, should the Texans win the coin toss, to choose the end of the field facing the stadium clock, which would give the Texans the wind at their backs.