By far the easiest options for moving large amounts of data between Pi Zeros and other Pis are USB OTG, which has already been covered by Dmitry Grigoryev's answer, and ethernet or WiFi.
While USB OTG will work great if your Pis are fairly close together, the run length specification for USB tops out at around about 5 metres. Further apart than that and the time taken for signals to move between devices starts to interfere with your data transfer, resulting in degraded performance.
Using ethernet or WiFi will involve a little extra expense, as you'll need to buy suitable adapters for the Pi Zero, but has a couple of distinct advantages:
- It will work equally well on all Pi models. If you decide at some point in the future to switch to using Pi 3s instead of Zeros you won't need to change anything about your setup. Going with USB OTG restricts you to Zeros (and possibly As).
- Using ethernet/WiFi, you can decide at a moment's notice to send the Zeros' video feeds/files directly to one or more machines somewhere else for processing and storage. As USB OTG is a short range 1:1 connection, you can't decide to send data to some other machine that's not nearby and connected via the USB cable. Whether that's an issue or not depends on your specific requirements, but it may be extremely useful to have the option to send video files/streams to a group of devices which are not in the same room, rather than a single device which is.
Speed-wise there's not much to choose between USB OTG and ethernet/WiFi. The way the Pi's put together puts a maximum limit of around about 20MB/s on any data transfers. Both approaches should provide you with similar rates.