  We continue studying a parabolic flow of almost K\"{a}hler structures
introduced by Streets and Tian which naturally extends K\"{a}hler-Ricci flow
onto symplectic manifolds. In the system of primarily the symplectic form,
almost complex structure, Chern torsion and Chern connection, we establish new
formulas for the evolutions of canonical quantities, in particular those
related to the Chern connection. Using this, we give an extended
characterization of fixed points of the flow originally performed by Streets
and Tian.
