I have read all their book in New 52 so far so i though this would be an interesting matchup..
Round 1: Morals on
Round 2 : Morals off (but for this battle, for whatever reason Captain Atom despite Morals off is not willing to go to Flash's past and kill his mother or stuffs like that, same for Flash if he's capable of it.. )
Win by Death, KO, incapacitation or BFR
fighting takes places on Earth minus all the population.
Starting distance: Flash is in America (New York) .. Captain Atom is in Australia (Perth).. both know where each other are.
For this battle both are familiar with each others powers to the extent they know them in comics and no more. I.e. Captain Atom knows flash is fast, and flash knows captain atom is powerful, but Atom doesnt know fempotsecond reaction time and BFR vortex from Flash and Flash doesnt Know Captain Atom's ability to time travel and teleportation.