Kinect data to a microcontroller
Even if you could get the data into an 8-bit microcontroller like an Arduino, it would be completely inadequate to process it. According to Wikipedia, the depth information streaming out of the Kinect is 640x480, 11-bits of resolution. That's about 600 kB of raw data for each frame, and the frame rate is 30 Hz. So, we need to crank through about 18 MB of data each second. This isn't too big of a challenge for a PC, but it's of the league of something like an Arduino.

Instead, you may have better luck using something like a Raspberry Pi. It has a 32-bit ARM microprocessor running at 700 MHz, 256 MB of RAM, and a GPU. It's basically a PC from 8 years ago on a single board.