Gone Girl is not part of a series. It is a one-off novel written by Gillian Flynn, which became a huge success when it was published two years ago in Summer 2012.
The book is the third one that Gillian Flynn has published so far. Because of its success, the stylised black and white/orange/red cover that her publishers, Crown, used for the cover was then used to relaunch her earlier books in the same kind of style:
A lot of series will use this tactic to sell books, making sure they're easily recognisable as part of that series for their main readers, so they can come back to the same character/s over and over. In this case, however, it wasn't a series Crown were promoting, but a writer.
Gillian Flynn is one of the few female writers to emerge with such success and acclaim in the past few years, and reprinting the books with the new cover meant more people would discover her earlier work.