Don't know your actual setup, but assuming all 3 movie clips are on stage, have different instance names, and are all stopped on a first blank keyframe, thus in fact invisible, you could start the first one, with a start button...
on(release){
_root.mc1_instance_name.gotoAndPlay(2);
}
Next, on the ending frame of this mc1, add the following...
_root.mc1_instance_name.gotoAndStop(1);
_root.mc2_instance_name.gotoAndPlay(2);
And on the ending frame of mc2...
_root.mc2_instance_name.gotoAndStop(1);
_root.mc3_instance_name.gotoAndPlay(2);
If you ever want to loop back to playing the movies in the same order, just add the following on the ending frame of mc3...
_root.mc3_instance_name.gotoAndStop(1);
_root.mc1_instance_name.gotoAndPlay(2);