"I'm very supportive of the team, but under no circumstances will the Dallas Cowboys - I don't care what happens - under no circumstances will we as an organization, coaches, players, not support and stand and recognize and honor the flag".
The NFL is not considering fining players or teams who choose to kneel, link arms or remain in the locker room during the national anthem, the spokesman added.
Multiple NFL players say they have been explicitly and implicitly warned against doing any kind of demonstration during the national anthem in the weeks following Donald Trump's directions to owners to "get that son of a bitch off the field" for protesting racial inequality.
"If there's anything that is disrespectful to the flag, then we will not play", Jones said after the Cowboys' loss to the Green Bay Packers.
Before the Cowboys' game at Arizona on September 25, Jones and members of his family joined the players, coaches and staff on the field prior to the anthem.
President Trump tweeted that he had asked Mr Pence to leave if players kneeled and said he was "proud of him".
NBC News reported Sunday that reporters were told before the game there could be "an early departure" by Pence. "He is receiving great praise for leaving game after the players showed such disrespect for country!"
On. Sept. 17, only six NFL players protested during the national anthem. "He's fired! He's fired!'"
Anthem demonstrations first became a hot topic of conversation in the National Football League last season when then-San Francisco 49ers quarterback Colin Kaepernick became the first player to partake. A number of players followed Kaepernick's lead by taking a knee during the anthem past year.
The act of kneeling before the flag and during the playing of our national anthem represents the highest form of respect, faithfulness and allegiance one can demonstrate.