Flowchart grounded dialog systems converse with users by following a given flowchart and a corpus of FAQs. The existing state-of-the-art approach (Raghu et al, 2021) for learning such a dialog system, named FLONET, has two main limitations. (1) It uses a Retrieval Augmented Generation (RAG) framework which represents a flowchart as a bag of nodes. By doing so, it loses the connectivity structure between nodes that can aid in better response generation. (2) Typically dialogs progress with the agent asking polar (Y/N) questions, but users often respond indirectly without the explicit use of polar words. In such cases, it fails to understand the correct polarity of the answer. To overcome these issues, we propose Structure-Aware FLONET (SA-FLONET) which infuses structural constraints derived from the connectivity structure of flowcharts into the RAG framework. It uses natural language inference to better predict the polarity of indirect Y/N answers. We find that SA-FLONET outperforms FLONET, with a success rate improvement of 68% and 123% in flowchart grounded response generation and zero-shot flowchart grounded response generation tasks respectively.