Legally, it seems pretty cut-and-dry. He could argue that the damages were unavoidable in the pursuit of saving lives, but then if I floored it to a crime scene in my car and smashed a bunch of cars along the way, it probably wouldn't hold up.
The only exception to this is during his actions as a member of the Justice League. I don't know that it has ever been explored, but the JL seems to have some sort of "official" nature. In Justice League Unlimited, Green Lantern mentions not being able to operate in certain countries, for example. Their relationship with the US Government, while rocky at times, is also often quite close, and they often act like they have official authority in their dealings with criminals and rogue governments.
If the JL has some kind of "authorization" or other official endorsement, damages from their fights may be the liability of the US Government or other agency. This would be equivalent to the way that an individual soldier isn't responsible for the damage done during a battle.
But other than that, there's probably no real defense for all the incidental damage done by many superheroes, Flash included.
...but it'll never happen.
One of the most charming elements of the Flash's mythos is his relationship with Central City. Simply put, they love that guy.
He's got a Flash Museum, and they hold Flash Appreciation Days. They don't fear him, like Gotham does Batman, and they don't even look up to him, like Metropolis does Superman. They love him like a pal, and they treat him like one.
In the Justice League Unlimited cartoon, Flash is shown offering medical advice to little old ladies, playing golf with random dudes, and even remembering individual citizen's birthdays. He goes all out to find toys for local orphans on Christmas. He's more than a boy scout, like Superman, he's everyone's best bud.
In the CW live-action show, Flash is shown painting houses, dropping off flowers for fighting couples, and more, in addition to saving people's lives on a daily basis. He's obviously just getting started as a superhero and public figure, but they're clearly building toward that kind of relationship with his city. From the pilot (in which Oliver Queen tells Barry he can be better than a vigilante because he can "inspire people") to the Season 1 finale (in which we catch a glimpse of the Flash Museum), the whole show seems very aware that the Flash will be beloved by his people.
So, even in a discussion of "superheroes being held accountable for their actions," I think the Flash would be the last superhero to be sued by his city. Frankly, they probably think of a broken window as an exciting sign that the Flash was nearby, and anyone grumbling about battle damage would likely be ostracized by his friends and community for being ungrateful for the Flash's service to the city.