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I created 3 flash buttons and linked them to the swf files
So you have three separate .swf's acting a buttons for the playable .swf's (totaling 6 .swfs, 3 buttons, 3 playable ones), or are these buttons actually inside the .swf's?
If I follow, the way to do this would be to have the "start" button within each playable .swf. It doesn't even need to be a button, really, a simple transparent box the size of the stage, converted to a button symbol, that executes play() when clicked. This keeps the entire functioning of the .swf contained within itself.