I can only talk about the Kodak PIXPRO SP360 (and 4K). They work as normal USB cameras. But connecting them via USB doesn't give them enough current to keep on forever (they drain more than they charge). Maybe fixable with some kind of powered USB cable?
I have a short experience with SP360 (firmware version 1.0.5). I think it is important to highlight the differences of SP360 and SP360 4K since AFAIK only the SP360 4K version appears as V4L2 device.
The USB interface in SP360 serves only for storage access purposes. The only way I have found to stream the live image is setting the cam in WiFi mode and sniffing the MJPEG stream. Some instructions on that can be found [here](https://richard.milewski.us/blog/?page_id=47). Since this stream is actually meant for live preview on a mobile app, the quality and resolution is far from the cam is actually capable of. Although the cam has an HDMI output, it is only enabled in playback mode and does not provide live feed.
The SP360 4K has a webcam functionality and enables live stream to HDMI (now the external capture cards are also an option).
I think @veiko was being too modest. Not only did he get the Kodak 360 camera streaming, he wrote RViz plugins to blend and display a spherical image (requires 2 cameras, ~1 hemisphere each) and use a VR headset.