It has nothing to do with the flexibility, but the flexibility is tied into the strength required to maintain these angles. Building the strength through the joints, you need to coordination of your lower body to lead the turn. If your knees and legs lack flexibility and strength you will probably not be able to hold a high edge angle, this includes your hips. The lower body is supposed to lead the turn effort, it works together as a system.. The exercise I have described is just one for people to try at home or in the office. When you're on snow you're obviously fighting gravity so the biggest this is extending yourself and maintaining contact with the snow.
This https://skimoves.files.wordpress.com/2014/03/forces-on-skier.jpg picture illustrates the forces on skier. You can see him making the c with his body, to counteract the forces, the hip is the biggest pivot point as you aware. Most people seem to think there is only one way to set yourself to hold a high edge angle. If you want to work on your edge angles, get out there and start carving rails, once you can begin touching your hand down while making a turn, you've got a high edge angle. Also having tuned skis would probably help to give additional grip.