High thermal conductivity (HTC) in polymers is a vital thermophysical property that significantly enhances industrial applications, such as modern electronics and electrical systems. Because of multiple degrees of freedom in polymer synthesis, it is impractical to explore HTC polymers solely through experimentation; hence, a predictive model for HTC is necessary. In this context, we emphasize polymer crystals, which are thought to represent the highest possible thermal conductivity bounds for real polymers. Here, the HTC polymer crystals were computationally discovered by using a data-driven method incorporating physics-informed screening with first-principles phonon calculations. Additionally, a less computationally demanding physical quantity associated with thermal conductivity was selected for the polymer crystals, and its correlations were investigated. A physics-informed descriptor was used to perform the high-throughput virtual screening of 1073 polymer crystal structures obtained from the polymer genome datasets. Through this strategy, we identified polymer crystals of polymethylenimine (PMI), poly(methylene oxide) (PMO), and polyamide (PA), with lattice thermal conductivities (LTCs) at 300 K of 21.81, 94.95, and 65.27 W/(m K), respectively. Moreover, the LTC of PMO exceeded 100 W/(m K) in the temperature range of 100-270 K. Additionally, the obtained results were further analyzed by examining phonon lifetimes, group velocity, mean free paths, and modal heat capacities of the polymer crystals, offering deeper insight into the fundamental mechanisms behind their thermal conductivity.