In the opening of the movie Watchmen, when Bob Dylan's "The Times They Are a-Changin'" is playing, there is a scene where a harmless teenage girl steps forward and tries to put a flower in a soldier's rifle's muzzle but the soldier shoots anyway. Is this scene based on real history? Was there a specific event that happened just like the movie showed?
The scene appears to be an homage to the classic 1967 photo "Flower Power" by Bernie Boston.
Flower Power is an historic photograph taken by photographer Bernie Boston for the now-defunct Washington Star. It was nominated for the 1967 Pulitzer Prize. Taken on October 21, 1967, during a march to the Pentagon, the iconic photo shows a young, long-haired Vietnam protestor in a turtleneck sweater, placing carnations into the barrel of a rifle of a National Guardsman.
Obviously in the original incident, the gun was never fired. In the world of the Watchmen, this is subverted.
The reference is clearly referring to to widespread trope of "peaceful protesters against the Vietnam war putting flowers in guns" (as @user7812 suggests in their answer through the trope is wider than a reference to just one iconic photo).
But the movie may be conflating this reference with other incidents that occurred during Vietnam War protests. An example would be the Kent State Shootings in 1970, when the National Guard fired on unarmed students protesting agains one of Nixon's exacerbations of the war, killing several.
And, don't forget, the movie's alternative timeline has Nixon surviving much more successfully than in the real world and actually winning the war. In addition to that, it is clearly shown in the alternative timeline that Nixon used a variety of nefarious techniques to defeat opposing and protesters (The Comedian was implicated in the Kennedy Assassination, Nixon's team killed the Watergate Journalists before they could publish the evidence that, in our timeline, destroyed Nixon's presidency). So the movie may be not just be conflating several historical incidences, but hinting that Nixon got away with much more brutal activities in his suppression of anti-war protest.
So the movie scene is not just conflating real history, but distorting it in a way that is entirely consistent with its alternative history.