I can understand the big three being the leads, but why Flash? I never considered Flash to be that popular.
Well, I put it down to those four being the most relatable characters in the JL. You have:
Superman, who represents masculinity, hope and the light. He is the ultimate example of compassion, just as anyone who wields great power is (be it physical, political, economical or otherwise), yet he doesn't abuse it, and still makes time for even the weakest of people. He also represents the "Jesus figure", in that he landed on Earth as a child (descended from the heavens), and is the son of a brilliant scientist (science which would be indistinguishable from magic to us) and a member of a highly advanced race (Gods).
Wonder Woman represents femininity, equality and nature. Her character also displays the more artistic side of humanity, the concept of expression and how something beautiful, can also be extremely powerful.
Batman could be seen as the dark side of humanity, yet carries a great amount of hope along with that dark side. He does whatever he must to bring people to justice - alive. By not killing, he doesn't fully descend into the darkness and this also conveys will and retention of self, despite the often horrific criminals that he deals with . Batman is both a symbol of fear and a symbol of security. He represents a balance, a personfication of yin and yang perhaps?
The Flash represents achievement and victory, something in which we see a great deal of in sport. Flash is the ultimate racer, he sprints ahead to his goal in record timing, leaving everybody else in his wake. He's a scientist, and thus personifies human progression in the field of science, technology and academics. He could also be seen to represent the need for people to take it easy, and not always rush ahead.
Take from this what you will, it's the best shot I can give at explaining why I perceive them as being more relatable than the other characters.