Before this thread starts to fall down the list, I thought I'd take a few swipes at the flow concept.
The three sports I've played most in my life are probably basketball, golf and table tennis (ping pong). Golf is by far the least flowing of the these three sports, as I understand it. Since flow is so important to me as a sportsman, golf has been a less suitable sport. I can't play basketball anymore, but find me someone who plays ping pong at about the same level as I do, and I can find that sweet spot of competition where I lose myself in the moment: moving, reacting and rejoicing.
You can try to break flow down into a number of specific categories, but I know what it is; that special feeling where one is reacting to the environment without conscious thought. I was a pretty good basketball player as a kid, and by the time I was 24 or 25 years old, I knew the game well enough that no conscious effort was required to play. I had transcended the whole thinking about how to play, as did most of the good players I played with. As a guard who had the ball in my hands a fair amount, there were times to run, and times to slow the ball down. When to assert yourself, and when to stay out of the way. Everything about the game became spontaneous and unscripted. After thousands of hours of practice and coaching, you just knew instinctively what needed to be done to win games. You didn't win them all, because there are lots of good basketball players, but we won our fair share.
Don't think, play the game.
The primary difference between basketball and golf is the speed in which decisions are made. In fact, professional golfers have proven that slow decision making and execution works best for optimal performance. Also, golfers initiate every action, and never react to an outside agency, such as a competitor. I found that elated state in sports by extreme physical challenge, coupled with unconscious reaction to a changing game environment, provided by a outside agency. Basketball has it, ping pong has it, and golf does not.
The only way golf could elicit a state of flow, as I understand it, is to be played quickly. The other day I played a quick nine with three other friends, in about 80 minutes. When you're playing fast, where no one takes more than 5-10 seconds to play his shot, you are fully engaged, watching the action carefully while also preparing for your next shot. It's your turn, go! That's a flow game, that's a rhythm game, and that's probably how we should always play golf.
Perhaps one can separate the flow of the actual playing of golf shots from the downtime between shots, where we shut the mind off by whatever method we choose. I like looking around, watching birds and animals, chatting during friendly rounds, less so during competition. I've had glimpses of a flow state during golf rounds when I was swinging it well, but once again, it doesn't match that endorphin high of working your ass off to keep up and making decisions on the fly.
I hope this makes some sense.