I kip when I'm trying to lace them together or if I'm on a bar, but I have studied them enough to learn some techniques, so here's some things I've learned for rings, especially with more strict muscle-ups:
1. as you start to pull up, focus on getting your "head through the window" sooner than you think you need to. By the point where your elbow is 90°, you should be rolling your body forward to get through the window. I picture my breastbone, or sternum. I'll never get my head through the window if it's facing upwards at all when my arms reach that point. There's just no room. This is really important when you're kipping. When you feel like you didn't kip high enough, your body wants to explode with your lats to pull yourself high enough, but if your arms are already past that 90° position, all you're going to do is pull your sternum toward the rings (picture doing a chest to bar pullup), but unless you can get the rings to your hips, you'll never be able to hold that position to get your head through the window. Start the transition earlier than you think. This is one part where a false grip makes things a little easier.
2. Don't cut the transition off too early. If you've reached the point where you can start the transition, you can finish the transition, usually. But if you try to start the dip before your elbows are directly above your hands, you'll be pushing the rings away from your center of gravity. Nothing is more frustrating than a no-rep after you get your shoulders over the rings. Get the transition, relax, and blast through the dip. It looks uncomfortable, but the bottom of the dip is the closest thing to relaxed once you start the muscle-up movement.
3. To get them unbroken, learn to relax as you drop from the top. Put your legs out in front of you, push the rings out in front of you, and just drop and relax, keeping a solid but loose grip on the rings. As you come toward the bottom, your legs and the rings will end up behind you, with your hips and shoulders out in front, and all you have to do is turn your palms away at the bottom, then snap them back to neutral to start the next rep. Consider having someone lift you to that top position, and start your first rep from there. The first muscle-up is the hardest when you have to lace them together, because you have to manufacture the momentum of the kipping motion. Once you get to the top of your first one, it's easy, the biggest problem from there is keeping the rings from swaying too much.
