Flame speed data reported in most literature are acquired in conventional apparatus such as the spherical combustion bomb and counterflow burner, and are limited to atmospheric pressure and ambient or slightly elevated unburnt temperatures. As such, these data bear little relevance to internal combustion engines and gas turbines, which operate under typical pressures of 10-50 bar and unburnt temperature up to 900K or higher. These elevated temperatures and pressures not only modify dominant flame chemistry, but more importantly, they inevitably facilitate pre-ignition reactions and hence can change the upstream thermodynamic and chemical conditions of a regular hot flame leading to modified flame properties. This study focuses on how auto-ignition chemistry affects flame propagation, especially in the negative-temperature coefficient (NTC) regime, where dimethyl ether (DME), n-heptane and iso-octane are chosen for study as typical fuels exhibiting low temperature chemistry (LTC). The computation of laminar flame speed of lean and stoichiometric mixtures of fuel/air was performed at different ignition reaction progress, by selecting the thermal chemical states corresponding to different residence times during auto-ignition as the flame upstream condition. Using scaling and budget analysis, it is shown that a well-defined flame speed for such a partially reactive mixture in the classical diffusion-reaction limit could still be feasible in the appropriate computational domain, especially with a sufficiently reduced induction length. The comparison of flame speed against different types of progress variables indicates a nearly linear relationship between the flame speed and progress variables based on the fuel mass fraction and temperature. Thermal and chemical effect of a cool-flame upstream has been isolated by comparing the flame speed of the initial mixture and that of the instantaneous mixture under the same thermodynamic conditions. It is found that the enhanced propagation is shown to be largely a thermodynamic effect, while chemistry nevertheless plays an overall retarding role. Sensitivity analysis has been performed to identify the key species which most influence flame propagation at different reaction progress. A general scheme of simplified mixture was constructed to describe flame propagation in a partially reactive mixture, for both lean and stoichiometric, as well as high pressures conditions. This study provides useful insights into flame propagation in practical engine conditions.