You would figure one bleeding-heart owner who hire him even to be the #3 or #4 QB on the team, just to make a statement. The issue here is Kaepernick wants a starting role or nothing. If he could at least read a defense at the college football level, he would have a job.
The issue for owners is once you hire the Kap, a team can never fire him.
Now that the situation has snowballed, I wonder if an owner would do that. They have an investment of hundreds of millions of dollars and huge expenses and payroll to meet. Keep in mind, they’re successful businessmen who reached that ownership level.
The NFL has a hard 53 person active roster limit. Before any team could sign him, they would have to first get rid of someone currently on the team. Possibly Brandon Marshall or some other concerned active player, in the spirit of solidarity, could solve that problem by voluntarily giving up their slot to make room for him.