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In this paper, based on the coupled-mode and carrier rate equations, we have derived a dynamic model for a linearly chirped distributed feedback semiconductor optical amplifier (DFB-SOA) all-optical flip-flop (DFB-SOA-FF) and analyzed it numerically. We have investigated the effects of assist light and cross-phase modulation (XPM) on the dynamic response and rise and fall times of the DFB-SOA-FF, for the first time. We have also shown that injection of an assist light, within the transparency spectrum, into a DFB-SOA with a linearly chirped grating can improve the device speed limitation, significantly. Values of the ON and OFF switching times for such an optical flip-flop, in an optimized condition, are found to be 190 and 195 ps, respectively. These show reductions of more than three times in the ON and seven times in the OFF switching times with respect to those of the uniform grating DFB-SOA-FF. Finite-difference time-domain method is used for numerical simulations.