If you duplicate the network frames of a "video stream" using port mirroring it might or might not work, depending on the protocols being used.
With TCP as a transport-layer protocol, a logical connection (a socket) is formed that requires both connection partners to actively participate. Accordingly, port mirroring won't work unless the monitor port listener is somehow happy with passive listening in on the connection of the real partners. How to do that is more a programming task and off-topic here.
With a UDP-based or possibly RTP-based stream, it is possible to have an entirely one-way stream, depending on the actual application-layer protocol on top (which is off-topic here as well). So, duplicating the UDP stream might work. If no in-depth documentation of the protocols is available you might just have to try.
In any case, you'll need to solve the likely problem with the duplicate distribution system address. You might need to set up various filtering on one port to prevent disturbances on the network or application level, again depending on the actual protocols. You may need to hire a network expert to set up those filters.
A more realistic approach would be to duplicate the stream on a fake distribution system (a kind of proxy) that in turn feeds the real distribution systems. Of course, this may be extremely protocol-specific and probably requires programming, which is also not in the scope of Network Engineering and off-topic here.
Also, as Ron has hinted, for a high-availability system you need to remove all single points of failure, requiring a redundant network setup.