Your Swim Kick...

Yup - should come from the hips.  You shouldn't be bending the knees too much.  A lot of runners bend their knees and flex their ankles, making the kick largely ineffective.

To practice an effective kick, practice kicking vertically in the water.  If your kick is effective, you should be able to keep your chin above the water without much problem.  You'll find that if you start flexing the knees too much, you'll start to sink.

You also shouldn't be creating a lot of splash with your kick when you are swimming.  The feet should be just under the surface of the water, using the water's resistance to push you forward.  If your feet are slapping the top of the water and making a huge splash, it's likely that you're bending the knees a lot.

It doesn't talk about core or where your kick is suppose to come from, but here's an article from one of my favorite sites that offers free swimming videos.  You can also click the video link on the top right hand corner to watch.

http://www.goswim.tv/drilloftheweek_comments.php?id=1558_0_20_0_C#