Finding amorphous polymers with higher thermal conductivity is important, as they are ubiquitous in heat transfer applications. With recent progress in material informatics, machine learning approaches have been increasingly adopted for finding or designing materials with desired properties. However, relatively limited effort has been put into finding thermally conductive polymers using machine learning, mainly due to the lack of polymer thermal conductivity databases with reasonable data volume. In this work, we combine high-throughput molecular dynamics (MD) simulations and machine learning to explore polymers with relatively high thermal conductivity (> 0.300 W/m-K). We first randomly select 365 polymers from the existing PolyInfo database and calculate their thermal conductivity using MD simulations. The data are then employed to train a machine learning regression model to quantify the structure-thermal conductivity relation, which is further leveraged to screen polymer candidates in the PolyInfo database with thermal conductivity > 0.300 W/m-K. 133 polymers with MD-calculated thermal conductivity above this threshold are eventually identified. Polymers with a wide range of thermal conductivity values are selected for re-calculation under different simulation conditions, and those polymers found with thermal conductivity above 0.300 W/m-K are mostly calculated to maintain values above this threshold despite fluctuation in the exact values. A classification model is also constructed, and similar results were obtained compared to the regression model in predicting polymers with thermal conductivity above or below 0.300 W/m-K. The strategy and results from this work may contribute to automating the design of polymers with high thermal conductivity.