Hi all. 3 stripe white belt here. I love getting to the North South position and getting the Kimura from here but I have a little difficulty on occasions where my oppo would escape,either by going flat or turtling. I know my position needs developing to avoid this in the first place but how do I proceed when this happens? Do I give up on the grip and attack something else that's easily available or just scramble or is there a way to keep the grip and move into another attacking position?
There are a lot of options once you have the Kimura grip. Let's start, even though you didn't really ask, with why you are losing the position. My guess, without seeing you roll, is that you are not gaining solid control of the head. The body follows the head, so if you don't let it move, you generally will not lose control of the body. Put pressure on the head and/or squeeze it between your knees and they will be much less likely to turn in the first place.
There are a number of options once your opponent starts to move, but here are a few that are relatively simple and direct. If they roll toward their back, the classic answer is to switch to Armbar. This does not require a lot of mobility to pull of and is pretty high percentage . I prefer to hook under the shoulder rather than stepping across with my bottom leg, but there are several ways to make it work.
If you have a solid Kimura Grip, it should be hard for them to roll to Turtle, as they are moving into the pressure of the shoulder lock. If they do so, try to bring their arm up behind their back and finish it much like a Hammer Lock. If they manage to get their hand to the ground, you are in a good position to move to Crucifix or simply let it go and reset.
My advice is to apply pressure in such a way that they can't turn to quarters. It is much easier to control one direction and be prepared to move to the other. Work to finish the Kimura then, if you lose it, smoothly switch to the Armbar.
As I said, there are other options, but this is a simple, effective series.