Any press is good press for a new sports league. Colin Kaepernick would certainly bring headlines.
The former NFL quarterback has been languishing on the free agent market for a while. If being a quarterback is important to him, the AAF is a new league looking for talent to bring them to the next level. Kaepernick took the San Francisco 49ers to the Super Bowl and that's the kind of talent the AAF needs. The "distraction" and "political" talk might upset some people, but at least they would know the league regardless if they watch or not.
There's a reason Colin Kaepernick is not playing on an NFL roster and the AAF doesn't want any of that smoke.
The AAF is still early in its existence. Causing a stir could be disastrous for the league's development, especially if people stop watching because of a polarizing quarterback. Kaepernick is already 31 years old and there's no reason for any league to take a risk on a player who offers no assurances of performing well.