I may have missed a revelation about who Earth 2's new Batman...but here are some of my possible ideas for who it is/isn't and my reasoning behind them...
Although DC may have "let it slip" that Earth 2's Batman is Thomas Wayne (via Twitter with a toy release) I am hoping that the representative simply assumed it was Thomas due to the similarity in their costumes. (Batman of Earth 2 and Flashpoint Thomas Wayne Batman)
Thomas Wayne:
Why: The costumes are extremely similar
Why Not: In the first (or second) issue of Earth 2 we see Bruce Wayne die, and his grown up daughter sent to the main version of Earth...first off all would the death of 1 parent at the hands of a mugger be enough to send Bruce Wayne on his journey to becoming Batman...if it was only his mother who died, then why would he grieve so deeply?...Secondly if Batman's (Bruce's) daughter is grown up...we can assume that if Thomas was alive he would be in his "later years" already.
Damian Wayne:
Why: With Damian being killed off in Batman Inc. 8, why not make him the new Batman of Earth 2?...Therefore if there ever was a crossing paths of Earth "1's" Batman and Earth 2's Batman then it could be an emotional sequence in which father and son reunite. Also this Batman is seen to use excessive force and is okay with killing, as was Damian when we first met him.
Why Not: Damian has yet to be mentioned in a single Earth 2 comic (to my knowledge) and this Batman seems older than Damian would be (if he was still 10 on Earth 2) in his current appearance.
Dick Grayson:
Why: With Nightwing's fate unknown at the end of Forever Evil, maybe this is DC's way of saying, "we won't tell you who Batman (on Earth 2) is, nor will we tell you what happens to Dick Grayson in Forever Evil...but they are vaguely connected" Maybe since Dick Grayson is such a popular character (and one of Dc's oldest) they will not simply kill him off, but kill him on the main Earth only for a different version of him to be the Batman of Earth 2. Also from the image above we see that the Pre-Crisis Dick Grayson was well...a big dude and from every image we have seen of the new Batman, he is well...a big dude.
Why Not: Dick Grayson has yet to be seen or mentioned to be on Earth 2.
Jean Paul Valley:
Why: In his short stint as Batman he was seen to enjoy the use of excessive force, as does the new Batman, and their personalities seem to be very similar.
Why Not: JPV has yet to be seen or mentioned to be on Earth 2.
Obviously by the reaction to this question (above) the person cared to Bruce greatly and is surprised to hear that Lois (Red Tornado) knows that his predecessor was Bruce Wayne.
**Also to support the Dick Grayson is Earth 2's Batman...look at his arm (Batman's) it almost looks as if he has some form of gauntlet on it, and the gauntlet is a signature piece of Nightwing's costume.**