Evolution of sunspot structure and photospheric magnetic fields are important to understand how the flare energy is built up and released. With high-resolution optical data, it is possible to examine in details the optical flows of the photosphere and their relationship to the flaring process. Using G-band and Stokes-V data obtained with Hinode Solar Optical Telescope (SOT), we study the sunspot motion and flow fields associated with the 2006 December 13 X3.4 flare in NOAA AR 10930. We calculate the centroids of the delta spot umbrae lying in opposite magnetic polarities, and use two different methods to derive the photospheric flow fields of the AR. We find that the shearing motion before the flare changes to unshearing motion associated with the eruption. A decrease of average velocity of shear flow is found to be associated with the flare, with a magnitude of 0.2 km s-1. As a related study, we also test implementing the recently developed differential affine velocity estimator for vector magnetograms (DAVE4VM; Schuck, P. W 2008) technique for the magnetic field observations obtained by the Big Bear Solar Observatory (BBSO) and Helioseismic Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Using this method to analyze changes of active region magnetic fields associated with flares may shed new light on the cause and effect of flaring process.