Accelerated and parallel synthesis of sequence-defined polymers is an utmost challenge for realizing ultrahigh-density storage of digital information in molecular media. Here, we report step-economical synthesis of sequence-defined poly(l-lactic-co-glycolic acid)s (PLGAs) using continuous flow chemistry. A reactor performed the programmed coupling of the 2-bit storing building blocks to generate a library of their permutations in a single continuous flow, followed by their sequential convergences to a sequence-defined PLGA storing 64 bits in four successive flows. We demonstrate that a bitmap image (896 bits) can be encoded and decoded in 14 PLGAs using only a fraction of the time required for an equivalent synthesis by conventional batch processes. Accelerated synthesis of sequence-defined polymers could also contribute to macromolecular engineering with precision comparable to natural precedents.