Conversational machine comprehension (MC) has proven significantly more challenging compared to traditional MC since it requires better utilization of conversation history. However, most existing approaches do not effectively capture conversation history and thus have trouble handling questions involving coreference or ellipsis. Moreover, when reasoning over passage text, most of them simply treat it as a word sequence without exploring rich semantic relationships among words. In this paper, we first propose a simple yet effective graph structure learning technique to dynamically construct a question and conversation history aware context graph at each conversation turn. Then we propose a novel Recurrent Graph Neural Network, and based on that, we introduce a flow mechanism to model the temporal dependencies in a sequence of context graphs. The proposed GRAPHFLOW model can effectively capture conversational flow in a dialog, and shows competitive performance compared to existing state-of-the-art methods on CoQA, QuAC and DoQA benchmarks. In addition, visualization experiments show that our proposed model can offer good interpretability for the reasoning process.