A Reddit user uploaded this picture of the DC Extended Universe version of Flash (played by Ezra Miller) in Injustice 2. Like Wonder Woman, the gear will probably be unlocked through the completion of increasingly difficult ladders in the Multiverse game mode.
A user on the Warner Brothers Games community forum also stumbled upon an image on the Google Play store of Justice League movie costumes for Batman (tactical suit), Cyborg and Wonder Woman. Nothing is official yet, but these costumes are also expected to make their way to the console versions of Injustice 2 through Multiverse events.
It is likely that there will be a world for each character (possibly excluding Wonder Woman) to unlock all of their gear.
There are rumours that Aquaman will receive his Batman v Superman: Dawn of Justice costume rather than his Justice League version, due to the similar designs of the BvS and Injustice 2 costumes so that the hitboxes will not greatly differ.
Official announcements from NetherRealm Studios and Warner Brothers are expected to come next week before the launch of Justice League.