There's History API that can get the user's history, but that API has no support on mobile. Looking at the WebExtension APIs, beyond history API, there's nothing that can get the user's previous history. Although, it's possible to record each url visited and then build a separate history.
Is it possible to get the file where history is stored on the device for a firefox android extension?
Since extensions only load on Firefox Nightly, recording a user's visited sites manually wouldn't sync when using Firefox Standard android browser.
No, it ain't.
Have to record tabs or network requests instead.