This is a browser based technology and browser file.io is not standard. So at this time is not supported. There are 2 things you can do.
1. There is a 3rd party plugin(ie not Scirra) that does what you want, but only if your using NodeWebkit.
2. When you "export" have a TextBox/TextArea, and do TextArea.setText(webstorage.asJSON). This will give you the string version of the same profile. I know it's not as nice as moving a file, but that's yoru option.
3. Yep, there is a 3rd. Is to store the profile online an share by somekind of custom key.