"Netflix operates its own content delivery network (CDN) called Open Connect. Netflix manages Open Connect from Amazon, but the storage boxes holding videos that stream to your house or mobile device are all located in data centers within Internet service providers' networks or at Internet exchange points, facilities where major network operators exchange traffic. Netflix distributes traffic directly to Comcast, Verizon, AT&T, and other big network operators at these exchange points."
Everything else - such as the Netflix UI, your account management, billing, etc - is on Amazon. But Netflix has an enormous amount of hardware distributed around the world. If you wanted to compete with Netflix, you would need to do a lot more than uses Amazon's cloud services.