SPOILER: he's not.
According to a fan theory (read: wishful thinking), in Batman v Superman: Dawn Of Justice, Ben Affleck isn’t Bruce Wayne – he’s just the man who took over the role of Batman after Christian Bale’s Bruce Wayne retired from crime fighting at the end of The Dark Knight Rises to wile away his days in Florentine cafes.
Then, at some point in the film, Christian Bale would turn up as the real Bruce Wayne, and he would then go on to take over the responsibility of Batman.
Somehow we don't think Ben Affleck would have signed up for that, and now Christian Bale has shot down the idea:
I haven’t heard that. This is the first I’ve heard of it. I think it’s pretty clear that Ben [Affleck] is playing Batman now.
When queried on whether he would play Bruce Wayne again, he responded with a four word shutdown:
No, it's not happening.
So, that unequivocally clears things up.