I've seen several threads about this issue. I did not experiment on this, though. Most of the threads contain references to OpenCV and specific/suported cameras. Some threads, not necessarilly the best ones:
An external ref. about Intel Galileo Gen 2 & camera:
I'm no expert on giving support, but I'll give it a try.
First. Are you able to set a terminal session for your galileo? (e.g. place where you can run your Linux commands)
if you can, could you please connect your webcam to Galileo and run this command dmesg | tail -10 and post the results please. (I wanna check first if your camera is being recognized)
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Were you able to connect the camera with the Galileo, what were your results in following the threads posted above? What have you configured so far?