merxlin,
Thanks for the endorsement.
Both those kick styles require strong glute muscles, and a lot of people don't have good strength there, which leads to lower back and knee pain. You also need hip flexibility as well so that you have good range of motion and body mechanics.
The prime movers in the traditional kick are your gluteus maximus and your hip flexors. You also use your rectus abdominus to stabilize so that you are not over-arching your back.
In our Yoga for Scuba Divers book, we include an exercise that strengthens these muscles with good form--I learned it from a physical therapist ages ago when I was working on on strengthening my glutes to help with some knee issues.
Walking lunges or static lunges are great ways to build strength there, but you have to pay attention. The quadriceps will often take over and the glutes will get lazy. The yoga poses that I find work best for glute strength are chair and warrior 1.
In the frog style finning, it requires strength in several muscles of the hip and thigh. To open the legs, you use the gluteus medius & minimus along with the tensor fascia latae. I find warrior 2 is an excellent way to strengthen them. The adductor muscles draw your knees together and chair pose is a good way to strengthen them.
But flexibility is crucial too. Most people have tightness in their hip flexors because they sit all day, keeping the muscle short. So while it's important to strengthen, it's also important to stretch the hip in all the planes of motion.
Here's a good online discussion I just found about the movements of the hip:
index 6
Good luck!