I haven't found a full race video, but I believe this clip picks up around the 750m turn, but does include some under-water shots where you can see his kicking rhythm.
Just a couple of quick comments, while his arm stroking is incredibly smooth and consistent (27-28 SPL, WOW!) it doesn't appear that his kick is always as evenly weighted or synchronized with his arm motion. Obviously, the relaxed 2, 4 or sometimes 6 beat-kick works well for him. The main difference I noticed was that (other than the last 100) his feet come rarely come up for air as he maintains a "low amplitude" kick relative to the other swimmers in the pool. I'm sure that's part of the reason he was able to make up over 2 seconds on the world record over the last 100 as he added a steady, propulsive kick and picked up his stroking rate.