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You don’t save as a swf, only as an fla. So the only way to get a .swf from an .fla is to do File→Publish and it will create a playable .swf of the .fla in the folder where the .fla is saved. You can also press Ctrl+Enter or File→Publish Preview→Any of the choices.
You can publish the game as an html page and swf, but there’s not way that I know of to publish something from flash directly into the .zip . Maybe if you opened up the .fla from within the .zip and republished that it would automatically publish to the .zip, I don’t know maybe you’ll want to try that out.