Now that Man of Steel has opened the door for a Justice League universe, the hurdle most often addressed by skeptics is the sudden surge of similar heroes across the globe. However, given Barry Allen's particular skills, it's entirely possible that he has been protecting the citizens of Central City and beyond without them ever being aware of it; only embracing a public persona and eye-catching uniform upon seeing Superman do the same.
Besides answering continuity questions from a chronological standpoint, that approach also allows The Flash to share thematic elements with the last son of Krypton - embracing a call to protect without fearing what those around you might suspect. In addition, Central City's acceptance of The Flash (founding a museum and holding parades in his honor) contrasts the paranoia and suspicions Superman deals with on a regular basis.
Of course, the biggest challenge of a Justice League film is explaining why the heroes would ever group together in the first place. With Barry's loss of his parents leading to a decades-long friendship with Bruce Wayne, and his strong moral compass and middle-America upbringing making him a trusted confidant of Superman's, the three justify a team-up film all on their own. From combat to character, it makes more sense for them to work together than apart.