Providing effective automatic essay feedback is necessary for offering writing instruction at a massive scale. In particular, feedback for promoting coherent flow of ideas in essays is critical. In this paper we propose a state-of-the-art method for automated analysis of structure and flow of writing, referred to as Rhetorical Structure Theory (RST) parsing. In so doing, we lay a foundation for a generalizable approach to automated writing feedback related to structure and flow. We address challenges in automated rhetorical analysis when applied to student writing and evaluate our novel RST parser model on both a recent student writing dataset and a standard benchmark RST parsing dataset.