AC is faster than N, but also does not travel through obstructions (walls, floors, etc) as well.
But to answer your question, it depends on your setup (is router in same or different room)? And do you have internet service fast enough to exceed what your current router offers? It depends on the model, but your router should offer somewhere in the neighborhood of 450 - 600 Mbps over N. Real-world performance is always less than what is stated on the box, but most people don't have that fast of internet service yet.
Does your current router give any problems streaming video on your Amazon Fire stick? If not, and like JackMDS already stated, there is probably no reason to replace your router. Regardless if you are connected on AC over N, you are still limited by your ISP speeds.