The problem of flow-induced crystallization (FIC) of polymer melts is addressed via a microrheological approach. In particular, the Doi-Edwards model with the so-called independent alignment approximation (DE-IAA) is used to calculate the now-induced change of free energy. Subsequently, the crystallization induction time, i.e., the nucleation characteristic time, is calculated in isothermal steady sheer and uniaxial elongational flows. Asymptotic, analytical expressions for the induction time are also derived in the limit of low and high Deborah number (the product of the deformation rate and the polymer relaxation time). The DE-IAA model is found to give more realistic predictions than those of simpler, dumbbell-like models already proposed in the literature. When compared to existing FIC experimental data in shear flow, good quantitative agreement is found with the polymer relaxation time as the only adjustable parameter of the model.