You could handle this inside of your key pressed object, and see use Logic to see if he has moved off of the stage width. For example, if your stage is 550px wide, when the x position of your character is greater than 550, then you would go to Scene 2. When the position is less than 0 - character.width then go to past scene.
This code currently works for two scenes. If you have more than this, you will need to add logic to determine which sceen you are in:
var amtMoved:int = 5;