A theoretical model has been introduced to elucidate the structure evolution and growth dynamics of macrophase separation in the styrene-block-butadiene (SB) diblock copolymer induced by thermooxidative reactions. In the model, the reaction kinetics is combined with the time-dependent Ginzburg-Landau equation (model B) using Flory-Huggins-de Gennes free energy density. Numerical simulations revealed that our kinetic model qualitatively captures the essential features of the experiments reported earlier, including domain morphology and spatiotemporal growth dynamics. Of particular interest is the existence of a plateau (or a hump) in the growth dynamic behavior governed by the competition between chain scission and cross-linking reactions.