Age data are critical building blocks of stellar evolutionary models, but challenging to measure for low mass main sequence (MS) stars. An unexplored solution in this regime is the application of probabilistic machine learning methods to gyrochronology, a stellar dating technique that is uniquely well suited for these stars. While accurate analytical gyrochronological models have eluded the field, here we demonstrate that a data-driven approach can be successful, by applying conditional normalizing flows to photometric data from open star clusters. We evaluate the flow results in the context of a Bayesian framework, and show that our inferred ages recover literature values well. This work demonstrates the potential of a probabilistic data-driven solution to significantly improve the effectiveness of gyrochronological stellar dating.