I'm having a little trouble understanding exactly what you're saying.
You say that, in your second method, you're kicking through your calf muscles, flexing and releasing your knees, so that the main movement is on your lower legs. But then you say that this reduces the bending in your knees. I'm having trouble envisioning how kicking primarily from your lower legs could result in less bending in your knees.
The main reason for kicking from your hips rather than your knees is to minimize the bending of your knees. A narrow, hip-driven kick produces less drag than a wide, knee-driven kick. It is also important to point your toes so that they're more or less in line with your lower legs, though your ability to do this may depend on your ankle flexibility.
A good drill for practicing your kick, if you swim in a pool where there is water over your head, is to go to the deep end and do vertical kicking. Fold your arms across your chest, and keep your head above water by kicking. You can transition to horizontal kicking by starting vertical kicking and then "falling back" onto your back while still kicking.
If you don't swim at a pool with water over your head, you can practice your kick by doing a drill called active balance looking up, in which you keep your hands on your thighs and rotate between your head lead sweet spot on one side and your head lead sweet spot on your other side (essentially doing backstroke without the arm movements). Since you will be propelling yourself using nothing but your kick, you will quickly learn what things make you move faster and what things slow you down.