If the NFL wanted to fire those guys....they could. They very easily could. There is no such mandate that an employer cannot limit the free speech of an employee on the job premises, in uniform, during work hours. In fact, the very opposite is true. They have every right to do so.
Trump is saying that if he was in charge of that business, he would fire them. The First Amendment says very clearly states that it is referring to "Congress" and not the private employer.
~Jeordam
Not much to disagree with, here, except the sentence I've bolded. Trump says that he wants an owner to fire one of these "Sons of b!tches". And then goes on to say that he knows some of the owners, and that one of them will fire someone over it.
A president who was anti-PC and supported free speech would not make such statements, just like he wouldn't support people getting fired for other political speech.
You're absolutely right that the NFL team owners can fire these guys, and maybe even that they should be fired, depending on how their protests affect the bottom line, but there's no difference in principle between firing these guys for this and Google firing memo guy.