Thanks for the replies guys.
For a more focused look at this particular attack, I'll specify that the "Kimura" is the BJJ name for the downward bent figure four arm lock as opposed to the uppward bent shoulderlock that is referred to in BJJ as the "Americana" or the "Paint Brush".
Since it is mostl commonly taught first from the Guard, we'll start there.
There are certain details that are very important, over and above the the hand positioning, to the successful application of a Kimura.
#1. Move your hips.
#2. Move your hips some more.
#3. When in doubt, the answer is probably in moving your hips even more.
If this confuses you, good. That's where all of your big game improvements start.
Look at the picture posted in the above link....
Everything looks correct, right? Guard position. Grabbing the wrist, sitting up and putting your other arm over the opponent's shoulder, figure four grip on your own wrist, sit back and crank the shoulder up behind his back, right?......What's missing? Hip movement.
Although the pictures detail how the Kimura is commonly practiced, they also indicate why the Kimure so commonly fails against someone with any knowledge of the move. Plainly stated, the move seems to go out the window against anyone with more than 2-3 months on the mat.
You have no leverage advantage when you are paralel and flat on your back. It is all muscle. How do you get leverage? Move your hips out on the side of the lock, way out, and get turned on your side (all the way, just like when you are practicing the shrimp drill). When your hips are no longer underneath his, but under the actual lock itself, you will have tons of leverage. Get closer to perpendicular and things will be a lot easier.
As far as finishing? Don't forget to keep your leg on his back or at the very least, on the back of his leg, to keep him from forward rolling and escaping. Just like the Omo Plata discussed in the other thread, the roll is the most common counter.