Delta (δ) sunspots sometimes host fast photospheric flows along the central magnetic polarity inversion line (PIL). Here we study the strong Doppler shift signature in the δ-penumbral light bridge of solar active region NOAA 12673. Observations from the Helioseismic and Magnetic Imager (HMI) indicate highly sheared, strong magnetic fields. Large Doppler shifts up to 3.2 km s−1 appeared during the formation of the light bridge and persisted for about 16 hours. A new velocity estimator, called DAVE4VMwDV, reveals fast converging and shearing motion along the PIL from HMI data, and recovers the observed Doppler signal much better than an old version of the algorithm. The inferred velocity vectors are largely (anti-)parallel to the inclined magnetic fields, suggesting that the observed Doppler shift contains significant contribution from the projected, field aligned flows. High-resolution observations from the Hinode/Spectro-Polarimeter (SP) further exhibit a clear correlation between the Doppler velocity and the cosine of the magnetic inclination, which is in agreement with HMI result and consistent with a field-aligned flow of about 9.6 km s−1. The complex Stokes profiles suggest significant gradient of physical variables along the line of sight. We discuss the implications on the δ-spot magnetic structure and the flow-driving mechanism.