While the NFL currently has a flex schedule setup where they can move games to different days, they do not have a system in place where they can switch game times on Sunday. That will change starting in the 2014 season according to ESPN’s Adam Schefter who reports that the league has passed a motion that will allow a new ‘cross-flexing’ schedule.
In short, if the league wants to switch the game time or network of a Sunday game (excluding Sunday Night Football), they’ll be allowed to:
NFL creating new weekly cross-flexing system for Sunday’s next season in which 1 pm games on FOX can be 4 pm games on CBS and vice versa.
It’s likely not a platform that will be used too often, but it allows the league to flex a game to an earlier or later start time on Sunday to avoid a potential conflict.
For example, if the league has two premier matchups scheduled for early games, they can opt to flex one to the later start time so the two games won’t compete against each other.