An accelerated logarithmic potential models the mean motion of stars in a flat rotation curve galaxy that sustains a wind system. For stars outside the galactic wind launching region, the asymmetric removal of linear momentum by the wind is seen as a perturbing acceleration superimposed onto the galactic potential. We study the integrability of stellar motion in an accelerated logarithmic potential. We use surfaces of section of the dynamical system to probe the integrability of motion. We provide numerical evidence that motion in an accelerated logarithmic potential is non-integrable. Large scale chaotic diffusion occurs for lower values of the projected angular momentum along the direction of acceleration and persists at all values of the angular momentum in the outer part of the galaxy inside the truncation radius where the galactic acceleration balances the wind-induced acceleration.