It is possible in theory, but not the way it is shown in the movies. First of all, the human neck is both strong and flexible, and unless the person is taken unaware (like in a car accident), will automatically tense up in response to pressure, making it even stronger. Second, even if you could muster enough strength to break a neck, unless the rest of the body was restrained you would just end up twisting their entire body around.
The only way to pull off a snapping someones neck snap realistically is by getting the victim in a full-body grapplehold, then stretching and twisting the neck until it breaks. You'd need to be very strong to do it though; flexibility alone isn't going to cutbe enough to snap it.
It may, however, be possible to break someone's neck with an impact instead of a twist. A strong punch or kick may generateproduce enough force, but only if the body was restrained somehow, so not really practical in a fight. It may be possible to get them in a hold and then throw yourself and them onto the floor with enough force to twist their neck to the breaking point, but this would involve more luck than anything. This may be the best option to use in a story though - makethis makes it basically a lucky flukematter of luck.
It won't be an instant-kill in any event;matter; even if you fully paralyze the person from the neck down they'll still be alive until they suffocate. More likely than not they won't be fully paralyzed and you'll instead be left with a paraplegic who is perfectly capable of talking (or screaming). Think about the possible results of car accident neck injuries from a car accident. Those are basically the results you'll get from trying to do this if you dont instant kill them.(You Won't So Please Don't Attempt This)
All in all, it's notthis isn't a very effective killing maneuver, even with brute force and extreme flexibility.