Having had relatively few (in other words two) quantifiable flow moments in sport myself - after a lifetime as an athlete - I find this a fascinating subject. Because those two moments stand out still as the most fun I've had while competing, I start out every season hoping that the athletes I coach will find themselves living a few seconds where everything comes together and they lose themselves in what they are doing. Or maybe fully experience what they are doing is a better way of putting it. The problem is that to be in that "zone", you really must be doing and not thinking (or at least not thinking about exactly how to do what you are doing). And, of course how you get to that point is the hard part because it takes a LOT of practice to have learned your art well enough to set it aside.
I do think I've figured out my biggest problem though. Once I get to the point where the skill or sport is ingrained enough for me to be reasonably successful and possibly approach a flow moment my mind wanders. As in: What shall I cook for dinner? Should I wallpaper or paint the hallway? Why on earth would anybody buy those platform shoes I saw in Allure? You get my drift....