Looks like despite rumors of Cavill being in The Flash movie, that film will instead be erasing him from continuity instead.
Multiple insiders are backing up what one leaker who has a proven track record with MCU leaks and leaked the plot of NWH a long time in advance has said:
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Thanks and best wishes!
The full series of tweets from MTTSH (as she did not thread them):
I don't usually tweet about DC stuff but I habe a friend who have seen The Flash and the movie will erase every movie Snyder has done. Man of Steel, Batman v Superman and Justice League never happened now. Erased from continuity. Affleck and Cavill are both gone
Supergirl now the main Supes of Earth. Keaton is Batman and Batgirl will become the new Batman after her film
Movie ends with Flash and Supergirl and Shazam forming a new Justice League.
I’m assuming Gadots WW is still involved going forward?
Yes
Looks like Cavill screwed himself out of a job by refusing to do the Shazam cameo.