Before we counter the spinning armbar, we've got to take a quick look at the mechanics of the position itself. In order to execute this technique, as soon as your partner has locked in a Kimura as you're passing the guard, you've got to first hide your arm in between your legs or by grabbing your inside thigh, so that your partner will be unable to simply finish the shoulder lock from the bottom.

Now, sliding away from your partner so that they follow you onto their side, just spin around behind them as per usual (a typical spinning armbar, like from knee on stomach). It helps a great deal to post with your far arm (left, as shown in the video), so that you can get much closer to your partner's hips. Because they're locked into their own Kimura grip, their armbar defense is going to be virtually nonexistent here.