In the current DCU, how much should they remember of their past incarnations?

[Restingvoice]

They tried that with 5G and it didn't make much sense either.

I think Johns had the right idea but questionable execution. Just say that the various 'reboots' were actually different earths. Pre Crisis, Post Crisis, Rebirth and Nu52. That's the most sensible explanation. Although that makes me wonder how that will affect Jeremy Adams current Flash run. Will Wally be on the 'Rebirth' earth or the Post Crisis Earth?

Rebirth. The Post Crisis Earth is done. Otherwise Tim Drake and his peers would be 20, and Jon Kent would be just 1-3 years old since he can only have been born Post Flashpoint.

While in the new post Superman Reborn continuity that still applies, he was born 10+ years ago, with Supermarriage and Death of Superman happening before that.