I'm using Firefox Addon SDK, and have already developed an Chrome Extension.
I was searching similar to function available in Chrome Apps Identity Feature in Firefox but was unable to do so.
I have been through Firefox UUID for browser, but as this can differ between devices, I need some id which will uniquely define a user rather than Browser.
I think what you are looking for is if the user has synced their Firefox to an account? Check out this page in firefox - about:preferences?entrypoint=menupanel#sync
Firefox has profiles but they are not user tied. This is an example of different profiles in Firefox - https://addons.mozilla.org/en-US/firefox/addon/profilist/