According to the Fort Worth Star-Telegram, the complaint, filed in Texas, maintains that Jones violated the act that prohibits employers from threatening workers for their "concerted activity."
On Sunday, Jones said that any Cowboys player who does anything to disrespect the flag "will not play."
The complaint by Local 100 of the United Labor Unions requests that the National Labor Relations Board investigate the situation immediately to prevent any illegal firings.
Wade Rathke, chief organizer of Local 100, told the Star-Telegram that the NFL has established that there is no condition of work that requires players to stand during the national anthem.
"Jones through his efforts to bully his playing workforce is attempting to unilaterally establish a previously nonexistent condition of work," Rathke told the Star-Telegram in a written statement.
It makes no difference, said Rathke, whether the penalty for a player is being benched or released.
The NFL game-operations manual says players "should" stand for the national anthem. NFL commissioner Roger Goodell sent a memo to all teams on Tuesday saying he and the fans "believe that everyone should stand for the national anthem."