That’s a good question, but no, you can’t use the Video Experimenter with a ChipKIT board. The Video Experimenter is very specific to the AVR architecture and the real heavy lifting to perform video capture, video generation, etc. are done in AVR assembly.
Always be careful when someone says “Arduino compatible”. They mean compatible at the most basic level (I/O). But many shields take advantage of specific features of ATmega microcontroller.