Although I find the concept of flow quite interesting, I'm not so sure about needing to invoke the flow state to explain motor enhancement from unrelated continuous movements. For example, one possible explanation for why continuous motion would improve learned movements like typing is that the motor cortex is typically used to model periodic movements as a dynamical system, and that short-duration movements are actually abnormal in a motor sense.
Consider how many of the movements we make are naturally periodic. Walking in particular is highly cyclical, but many other types of movements that we typically make (e.g., swinging the arms to counterbalance the trunk during walking, counter-rotating the eyes, head, and spine during a turn-to-look movement, opening and closing the jaw while chewing, inflating and collapsing the ribcage during breathing) show significantly periodic activity. This periodicity suggests that one could model these movements as a rotation in an abstract "phase space" defined by the differential equations that capture the dynamics of the movement. Seen from this perspective, cyclical movements are the norm for almost any animal, whereas short-duration, "single-use" movements like typing or playing the piano are rather unusual. It could be the case that if the motor cortex (or even the basic movements encoded in the spinal cord) is inherently tuned to modeling cyclic movements, then adding some continuous motion could help the motor cortex capture the intended typing or playing movements as part of the larger, continuous movement.
These references don't address the specific topic at hand, but they do address the periodicity of the motor system at a relatively low level. I would argue that this periodicity should be considered "normal" for movement modeling. Whether or not this periodicity is useful for enhancing other movements is, as far as I know, not known.
M. Churchland et al., "Neural population dynamics during reaching," 2012 Nature http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3393826/
A. Ijspeert, "Central pattern generators for locomotion control in animals and robots: a review" 2008 Neural Networks.
Neural correlates of flow
It's quite difficult to map between levels of abstraction as widely separated as neural activity and a "meta-cognitive" state like flow. However, a quick search online did reveal a couple of papers that have attempted to relate flow to physiological measurements like EEG :
D. Kramer, "Predictions of Performance by EEG and Skin Conductance," 2007 Indiana Undergraduate Journal of Cognitive Science -- not sure where this journal is published, but it seemed like an interesting article
M. Klasen et al., "Neural contributions to flow experience during video game playing" 2011 Social Cognitive and Affective Neuroscience, http://scan.oxfordjournals.org/content/early/2011/05/19/scan.nsr021.full