+1 I would love to have that button in the "Translate Selection into <language>" pop-up as it often offers to translate into the text's original language (e.g. Translate Japanese text from English into Japanese which doesn't make sense).
Google Translate has this button that I actually use quite often.
Additionally, it would be important if, when working with 3 or 4 languages, the list of recently used languages (let's say 5 languages, plus an `about:config` option for the number of languages) were displayed at the top as "Favorites" in both the source and target languages (this speeds up workflow).
I would also appreciate having "about:translations" as a button for a custom toolbar (opening in a new full-screen window).
The need for this stems from Mozilla trying to be smart.
If I translate a Thai page to English, but then I open an English page, Mozilla tries to be smart by changing the default options to Translate English to Thai.
So the most common need I have is to reverse it back to Thai to English.
This UX wasn't very well considered, It should remain at the previous setting of Translate Thai to English. It is very rare that I will Translate English to Thai (I can't read Thai). Firefox places too much faith in the site language metadata. If I click Translate on an English site, it is 99% because I need to translate non-English content into English (e.g. English setting might make English menu options, but content and/or comments are in Thai etc).
I think that would negate 90% of the need for the flip (but it definitely would still be valuable).