Most rumors surrounding The Flash argue that the film will be adapting some elements of Flashpoint, the time-traveling narrative that relaunched the DC Universe into the New 52, though it's debatable how much of the storyline will end up featuring in the final film. Some expect to see Bruce Wayne's father Thomas, played by Jeffrey Dean Morgan, arrive in the cape and cowl to unleash pain upon the criminals of Gotham in some gritty dystopian future The Flash will create. Other reports indicate that Michael Keaton's Batman might appear in the film, indicating that the Tim Burton universe might become canon as well.
However, it's possible that another iteration of Batman might end up appearing in The Flash film. While all signs currently indicate that The Batman will exist separate from the rest of the DCEU, there is a distinct possibility that The Flash might be the means through which Robert Pattinson's Batman joins the ranks of Henry Cavil, Gal Gadot and the rest of the Justice League.
FLASHPOINT RETCON
The most obvious way this transition can occur is if The Flash ends up retconning or rebooting the DCEU. While it might seem problematic to reboot the DCEU only a few films in, it's possible that film might feature some element of Flashpoint in order to iron out any wrinkles in DCEU continuity that might've occurred during the franchise's early growing pains following Batman v Superman: Dawn of Justice.
In this situation, The Flash might alter the continuity of the mainstream DCEU to better align with the world of one of its popular Elseworlds stories. This means that the modern Batman might be altered to better align with The Batman's continuity. This means that they might recast characters like Commissioner Gordon or Alfred to better align with their iterations in The Batman, shift the timeline slightly to justify these newly introduced characters, etc.
The most noticeable way this can happen is if Thomas Wayne's iteration of Batman does something to alter the growth and trajectory of the past or if he says/does something that inspires the Flash to alter the timeline slightly in some way that has greater ramifications on the future -- namely, something that would keep Batman from becoming exactly like Ben Affleck. Most notably, however, this would mean that Robert Pattinson could show up as the current, mainstream Batman, replacing the retired Ben Affleck in the role for future appearances by the character.
MULTIVERSE MINGLING
However, the more likely reason why Robert Pattinson might appear in the DCEU is due to some form of multiverse mingling. While Thomas Wayne as Batman has been rumored throughout The Flash's pre-production, recent news indicates that The Flash might feature some multiverse mingling in the DCEU. Michael Keaton will be appearing as Batman in the film, continuing the continuity from the Tim Burton era of films.
This means that The Flash might end up wandering into Robert Pattinson's continuity, possibly bringing multiple iterations of Batman together in order to confront different iterations of the character. Perhaps the film might offer a moment where The Flash's Batman is obliterated in some fashion -- especially if Affleck ends up appearing. As a result, Pattinson, by necessity, is brought over from one continuity into the modern continuity. Perhaps Thomas Wayne's iteration of Batman meets with Pattinson's, emotionally bonding with his son. This union could potentially motivate Batman to travel into the future to handle the threat of Darkseid or some other cosmic threat plaguing the DCEU.
Another possibility is that The Batman continuity and the mainstream DCEU Continuity are blended together by the film's conclusion, thus retconning the DCEU into this new iteration. This decision would not only allow Pattinson to become the mainstream version of the Caped Crusader in the DCEU but also allow Matt Reeves to create a new Joker that could completely supplant the Jared Leto version, thus sparing any future Batman or Harley Quinn related film from Leto's presence.
Of course, there's always the possibility that, if Pattinson appears in The Flash, it would only be for a cameo and not a canon-altering event. Even so, this would still open up the door to future communication between the continuities that could evolve into something more should The Batman prove popular enough. In any event, it at least will demonstrate that the creators behind the DCEU films are not afraid to play with their own continuity.