How does ‘flow’ compare to ‘mindfulness’?
The American psychologist Mihaly Csikszentmihalyi is the discoverer of a mental state that he calles ‘Flow ‘. Csikszentmihalyi has researched this mental state for several decades and has published a great deal on the subject. In his books, Csikszentmihalyi writes extensively about Flow as the optimal psychological experience; e.g. as a violinist, when he has just finished playing in a concert in retrospect realises: “Wow, I was really in good shape there!” When somebody is performing a challenging task that is just within his reach of competence, he sometimes, not often, can get completely absorbed by what he is doing, forgetting himself or his surroundings becoming one with the action, as if the ‘Self’ dissapears and the consciousness of the person in the ‘Flow’ state is not disturbed by thoughts that are not relevant to the task at hand. When the Flow-state is over, usually after an hour or so, the person can see back and realise that he has been very productive and has overcome difficulties and made considerable progress. Once you have experienced Flow, it really makes your day and you feel very happy and on top of the world.
In Buddhism there is a comparible mental state, called Sati or mindfulness. Here’s a definition, taken from www.vipassana.com
“Mindfulness is nonconceptual awareness. Another English term for Sati is ‘bare attention’. It is not thinking. It does not get involved with thought or concepts. It does not get hung up on ideas or opinions or memories. It just looks. Mindfulness registers experiences, but it does not compare them. It does not label them or categorize them. It just observes everything as if it was occurring for the first time. It is not analysis which is based on reflection and memory. It is, rather, the direct and immediate experiencing of whatever is happening, without the medium of thought. It comes before thought in the perceptual process.”
According to experts, the Buddhist concept of Sati and the western scientific notion of Flow are one and the same thing. What is great though, is that the ancient Buddhist tradition delivers us dozens of techniques and hundreds of exercises to improve our concentration and to help us achieving Sati more often and longer. I am convinced that trained meditators can get into the Flow state more easily and can use this ability in their work or study. So start meditating! Here’s an article by George Boeree to start you off Buddhism.
Happy meditating 
P.S. I found a great article about Flow on this Buddhist site.