I also am not sure of the proper way to update this board, either. As far as I can tell it only has one USB connector which is connected up to UART2 (with Arduino IDE this would be Serial2).
There is no connection for the actual USB port of the Edison. For that you would probably need a different sparkfun module, like: DEV-13045 which looks like it is not released yet.
Again as deium mentioned, maybe someone at Sparkfun has an idea.
The only Ideas I have could leave you in a very bad state. Something like, what is mentioned in:
How to install a kernel from my repo onto Edison with the official image
But again I have no idea what state this would leave you in...