At least to me, when I thru-hiked te AT, the experience I had regarding "flow" had more to do with becoming more tuned in to nature and its natural cycles and my own physiology. This experience did not come on for well over a month, maybe two. Unlike runner's high, which was a frequent occurrence, the flow of long distance backpacking has much to do with becoming "tuned in." As you forget the ring of a phone, the sound of traffic, calendars, clocks, appointments, deadlines, stress, etc...slowly the more natural and basic needs of the body and mind are more apparent. Food when hungry, water when thirsty, rest when tired, companionship when lonely, and maybe a couple others. I was able to return at least in some sense, to living in a much more "real" and less "fabricated" world. Simplicity has much to do with it IMO. As the details from the less important, nonsensical, daily grind fade into the background, they are replaced with more basic instincts, more raw emotion, and certainly a much more physically in tune body. My senses of smell and hearing heightened significantly. My body rose and slept with the sun, and before long, miles were just miles, the number no longer made much difference.
I believe that the "flow" experienced by long distance backpackers has much to do with a cleansing or a washing away of those details of daily life that often mask the more basic human needs and block energy flow in the body. Feeding those basic needs is a very natural process and I think that can be felt as it is achieved.
We are from the earth. Long distance backpacking takes us close our roots again through a physiological, emotional, physical, and spritual journey. It does not happen overnight or even in a week of intense physical activity, at least what I am describing. It involves more than the exercise. It is also a truly humbling and wonderful experience.
Others may have different experiences with this - to be fair, my partner and I thru-hiked in much solitude. We were very late season south bounders who thru-hiked late into the winter and as the days grew short, our encounters with other people became more infrequent. Solitude was a big part of our journey.