I asked the Wise Masses at the jiujitsugear forum what they thought about defending the kimura attack from inside the closed guard. There were, typically, a number of good responses. The best, maybe, came from the "Vanilla Gorilla", Rick MacCauley, an Abu Dhabi Combat Club veteran:
If he had a kimura on my right arm I would stand with my right leg and grab the inside of my thigh with the arm getting kimura'd.Like I said, it's been a while since I've really had to fight off a kimura. Even then, most of the kimuras I've been attacked with have come from guys who've gotten dominant position on me (i.e., side control or north/south).
While doing this, I would be controlling his hip with my left hand by holding his belt and pushing down. If it was no gi, (I would control his hip by) just pushing down like I was posturing.
Key #1 to this escape is keeping your elbow into your side while grabbing the inside of your thigh.
Key #2 is that your hand not getting kimura'd has to keep his hip controlled, flattened and square to your body if possible so he can't generate power with his hips. This also prevents him from swiveling for other submissions (i.e., hopping a triangle or going for a "belly-down" armbar).
Still I want to start thinking of escapes insofar as being able to know your basic escapes is a big part of being a blue belt in Brazilian jiu jitsu as far as I'm concerned. Additionally, I'd like to start working the kimura into my set of attacks from closed guard (especially the "Werdum Series", that includes the judo armlock, crossover sweep, pendulum sweep and the kimura).