Wikipedia describes flow one way as "the mental state of operation in which a person in an activity is fully immersed in a feeling of energized focus, full involvement, and success in the process of the activity."
In parkour one can achieve a flow like this where you are totally immersed in movement and everything seems to tie in together. It's almost like time slows down and unusually higher physical performance may be achieved.
To achieve this flow you must have certain components:
1. You must have clear goals in mind.
2. A high degree of concentration is involved.
3. Balance between ability level and challenge (the movements are neither too easy nor too difficult).
4. Distorted sense of time, one's experience of time is altered. This is where you feel the time slowing down and you can not only focus on each individual movement, but, then how they will all tie together to make a beautiful picture.
There are countless other factors, these are just ones i thought were higher on the list. And not every factor needs to be considered to experience this "flow." But the point is that you want your movements through the area your working with to flow and have this sense of fluidity about them. Your body is the paint brush and your environment is the canvas. Your movements are the brush strokes over the canvas. To make a beautiful painting you want to be fluid and not choppy or unorganized with the movements you put down.
There are many by products to experiencing this flow. It is definitely a positive force that motivates you to develop your skills and movements more so you can create this flow and make a series of movements just one. Flow makes you perform at a higher level and therefore motivates you to always be as best as you can.
Here King David defines parkour as water or fluid motions linking themselves together.
And here Bruce Lee says to be like water and formless and allow your surroundings to help create your form.
I hope this learned you folks well.