In a way, Flash can be used as a level editor... Generally what people do is make the engine; assign responsibilities to each object (in code) and then they 'design' each level on a separate frames by visually dragging objects on the screen and assigning names.
Personally, I don't like using frames, I prefer just coding everything from scratch... I like to keep an array of LevelData objects for each level and then I pass it as an argument to my Game engine when required... For creation, I would make a separate flash file that acts specifically as a level editor; so I would drag shapes in place and when I'm done, I would get it to print data representing the configuration of the game for that level... I would then copy (ctrl+c) that data, go to my game.fla, instantiate a LevelData object using that data as an argument, then I would put the LevelData in an array representing a list of all the levels; all this is done during the game's initialization.
Flash games aren't usually complex enough such that you'd need to store game data in an external file.