The hip turn is something I have been struggling with for some time. I don't know if it is my flexibility or why exactly. During practice swings in front of a mirror, I can make a good hip turn, but whenever I try to get the hips moving on a real swing, my right leg tends to straighten and my weight seems to move a little bit forward towards the target, or almost no hip turn at all. One thing I have been working on that seems to work a little bit is for me to try and drop my left shoulder more down in the backswing ( more down, less around). It seems to automatically force my hips to move more. Does this make any sense. As far as flexibility goes, I tend to have very tight muscles in my hamstrings and glutes. I stretch these as much as I can.
Yes, that does make sense. That makes your shoulder turn a little more vertical, which makes room for the right hip to work more up and that gets it deeper. If the right hip works more up, there is more room for the right elbow to get in front of the hip on the downswing, you are more linked up and should be less "flippy" as you said n the OP.