I'm not familiar with the internal anatomy of the Kodak Stereo, but I've got a camera (Wirgin Stereo) that uses the same format, and I struggled with the same thing on the first couple of rolls. Eventually I realised that there was a little lip on one of the film rails that was supposed to serve as a guide to keep the sprocket holes on their sprocket, and if I tucked the film under that guide as I was supposed to, the frames lined up nicely. You may have something similar.

Mine puts two frames between each pair: e.g., 10 goes with 13, 11 goes with 8, 12 with 15. Yours is the same frame format and I believe the same lens separation, so it seems like you should get the same thing.
(The Wikipedia article at http://en.wikipedia.org/wiki/Kodak_Stereo_Camera agrees, with pictures of what a strip looks like.)

-NT