Fundamentally the Flash is a difficult character to adapt, as his history from the comic books draws heavily from what has become known as the Flash Legacy, a mythos that has become both a blessing and a curse for the character. Here, Wally West is the third man to take up the mantle of the Flash, with Jay Garrick (the Golden Age Flash) and Barry Allen (the Silver Age Flash) coming before him
and this doesnt even take into account the presence of Johnny Quick, Max Mercury, Jesse Quick, Impulsea literal army of speedsters that spans hundreds of years, with each of them connected to the Speed Force, a fundamental energy source that all speed-related individuals tap into. While it is true that this mythos does provide a rich tapestry for writers to draw upon, it also holds the character back, as most modern-day Flash stories seem to be mired in it (in the comics, Wally West fights crime as the Flash in memoriam of Barry Allen, who died in 1985's Crisis on Infinite Earths series, and is constantly in his shadow). As a result, readers often see the current Flash as nothing more than an extension of the mythos and not as an individual character; as he races through the pages of his monthly comic he drags his back-story behind him.
To combat this, the creative team took a big risk by severing Wally Wests ties to the Flash Legacy. On Justice League Wally is the only superhero to ever bear the identity of the Flash, and this distance from the mythos allows the character the chance to be something that he has never been able to be in his previous incarnations: unique. He doesnt have to operate in the shadow of two prior incarnations; he is free to live his life without being compared to another hero. And while comic fans have complained about the absence of Jay Garrick and Barry Allen, their omission provides Wally the opportunity to be his own man.
In keeping with the concept of Wally West being the only Flash, it should come as no surprise that, without a mentor in Barry Allen or the presence of the Teen Titans to hone his skills with, the creative team decided to make his character fill the category of the rookie in the teams dynamic. Portrayed as still learning the full range of his abilities and being inexperienced in terms of sacrifice (his bewilderment over Wonder Womans banishment in "Paradise Lost," his inability to comprehend leaving a teammate behind in "The Savage Time" or in "Hearts and Minds"), the Flash provides an interesting contrast when compared to his more seasoned teammates, who have been doing the job for years (and, in some cases, for centuries). In truth, the character is more Kid Flash than regular Flash, and the opportunity to see his evolution as a hero sans Barry is a new wrinkle for an old, Silver Age character. In addition, his lack of a mentor provides Wally with a measure of uncertainty when it comes to what his powers are actually capable ofas shown in "Only a Dream," the thought that his powers may one day lock him into super-speed mode permanently is one that will keep him awake at night for years to come.
On Justice League, the Flash is frequently portrayed as being an everyman, a peoples superherounlike the others, the Flash is the one that the public is most likely to run into on the streets and interact regularly with (whereas Batman is more likely to stick to the shadows, and the others can fly). Hes also more approachable, spending his spare time flirting with women in diners and visiting children in orphanages. These attributes make him indispensable to the team, as he provides a vital link between the Justice League and the community they serve (although it can also be a detriment, as he learned when he tried marketing his persona in "Eclipsed").
As for his relationship to the team itself, the Flash shares a vital symbiotic relationship with the Justice League. On one hand, his friendly and easy-going personality serves as the glue that holds the organization together. Over the series duration, hes managed to befriend every member of the team on some level; from his Oscar-and-Felix friendship with Green Lantern to the sarcastic remarks that he regularly trades with Hawkgirl. Through these relationships the Flash becomes a window with which we can get to know the other characters; in truth, hes a better peripheral character than Batman is because his extraverted personality. On the other hand, in exchange for these benefits, the Flash is unconsciously forced to become a better hero by his association with the others. Consider the evolution of his characters abilities: in Season One, the Flash was frequently seen being taken down by debris or by a slower target or simply doing something that undermined his status as a hero (one of the worst being his inability to pilot the Javelin-7 in "In Blackest Night"); while, in Season Two, he appears to have improved in his overall performance, piloting the Javelin-7 successfully in "Maid of Honor" and using his speed-related abilities in new ways (such as tricking the Justice Lords Batman into believing his heart had stopped in "A Better World"). Overall, he is, literally, the heart of the League (as it was alluded to in "A Better World"), as his presence provides levity to the teams mindset, as well as a measure of pride in his development.