If you use "Save File" instead of "Save," you can choose where to store the saved file. On my computer, the "Save" files are stored here: C:\Users\<username>\AppData\Roaming\Macromedia\Flash Player\#SharedObjects
I'm on a Windows PC. I don't know where it would be stored on a Mac.
However, on my computer, my "Saves" are deleted when the browser is closed, but that might only be because I have my browser set to clear all caches and history when the browser is closed.