The next generation of multimedia applications will require the telecommunication networks to support a higher bitrate than today, in order to deliver virtual reality and ultra-high quality video content to the users. Most of the video content will be accessed from mobile devices, prompting the provision of very high data rates by next generation (5G) cellular networks. A possible enabler in this regard is communication at mmWave frequencies, given the vast amount of available spectrum that can be allocated to mobile users; however, the harsh propagation environment at such high frequencies makes it hard to provide a reliable service. This paper presents a reliable video streaming architecture for mmWave networks, based on multi connectivity and network coding, and evaluates its performance using a novel combination of the ns-3 mmWave module, real video traces and the network coding library Kodo. The results show that it is indeed possible to reliably stream video over cellular mmWave links, while the combination of multi connectivity and network coding can support high video quality with low latency.