The Botball Chumbys have the driver microdia.ko, which seems to work okay on them. Unfortunately, I'm not sure how their libraries are accessing the camera, and they don't seem particularly interested in helping me. It's standard Video4Linux, but when I compiled various V4L programs for Chumby, they all either segfaulted or gave errors. If you're willing to put up with 160*120 resolution, and you don't need to use the screen while running your camera code, the Botball cbcui program can write a camera image to the Chumby framebuffer, which you can grab using the Chumby screen grabber program. The Botball Chumbys have a breakout board attached; I don't know how cbcui will behave if the breakout board isn't present. It's worth a try.
If you'd like a copy of the Botball Chumby firmware image, you can probably ask the botball.org people; there's a good chance they'd be willing to give you a firmware image.
If you happen to find a way to read raw images from the microdia camera at a higher resolution than 160*120, please do let me know. I've been trying for a month or so, with no success. :-/