No it is not his right. The First Amendment has nothing to do with this.
The First Amendment protects the individual’s free speech against the government. This has nothing to do with the government.This is a pro football franchise. And he has the right to have his feelings, but that team has the right to kick his butt off the bench and to fire him. He can still have his feelings, but he can have them somewhere else. So, this isn’t about the First Amendment or free speech.
Did you ever wonder why nobody in the NBA takes a knee? Answer: because they don’t allow it in the league.