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Flow cytometers are a vital tool for cellular phenotyping but are primarily limited to centralized laboratories due to their bulkiness and cost. Significant efforts have been made to construct on-chip flow cytometers for point-of-care applications, and a promising approach is filter-on-chip flow cytometers utilizing the conventional Bayer RGB filter on imaging cameras to miniaturize key optoelectronic components. However, conventional RGB filters fail to provide spectral channels of sufficient diversity and specificity for accurate identification of fast-moving fluorescence signals. Here, we present an optofluidic system with integrated metasurfaces that serve to increase the number and diversity of the spectral channels. Inverse design of spatially coded metasurfaces is used to maximize the classification accuracy of spectral barcodes generated along the particle trajectory obtained from single-shot imaging. The accuracy of this system is shown to be superior to generic RGB filter approaches while also realizing classification of up to 13 unique combinations of fluorophores, significantly enhancing the capability of portable flow cytometers.