Nope, it's purely fiction. Here's a link to an interview with the director.
Interview with Robert Zemeckis
Matt McDaniel: What was it about this project and the script in particular that grabbed you?
Robert Zemeckis: Well, whenever a really good screenplay comes across your desk, you have to do it, and that's what the situation was with "Flight." It was great, great screenplay.
MM: It's unique -- it's at least for Hollywood today -- that it's not based on a book or a comic book or TV show. Was the originality part of the appeal?
RZ: Yeah, of course. It's not, as we say, a pre-sold title. So the fact that it's very unique and original was very appealing.
MM: Was it inspired by true stories, or where there elements of truth that were worked into the movie?
RZ: No, it's completely fiction. The movie draws from different incidents that involved airplane malfunctions from the last couple of decades, but [there is] nothing that it's based on that's a true story.