This can be recreated by deleting any non-english language files and purging the cache, then by adding language files and making the new one available, thus activating the language drop-down select, which will not have any flags showing. Nor are flags shown in the Account Settings screen (Preferred Language dropdown).
If you log out and view as a guest there are flags but upon logging in again the flags are gone. On a separate browser I was logged in as a regular member and that screen also had no flags.
Purging either cache (general or language) or hitting the browser's F5 key on its own does not resolve.
The fix is to purge the 'general' cache and then hit F5. In doing this the flags are shown in both dropdowns.
@txcas would you please let me know if this fixes the flags for you.