ABSTRACT Applying our recently developed generalized version of the high-latitude emission theory to the observations of X-ray flares in gamma-ray bursts (GRBs), here we present clear observational evidence that the X-ray flare emission region is undergoing rapid bulk acceleration as the photons are emitted. We show that both the observed X-ray flare light curves and the photon index evolution curves can be simultaneously reproduced within a simple physical model invoking synchrotron radiation in an accelerating emission region far from the GRB central engine. Such an acceleration process demands an additional energy dissipation source other than kinetic energy, which points toward a significant Poynting flux in the emission region of X-ray flares. As the X-ray flares are believed to share a similar physical mechanism as the GRB prompt emission, our finding here hints that the GRB prompt emission jets may also carry a significant Poynting flux in their emitting region.