Flowchart-grounded troubleshooting dialogue (FTD) systems, which follow the instructions of a flowchart to diagnose users' problems in specific domains (eg., vehicle, laptop), have been gaining research interest in recent years. However, collecting sufficient dialogues that are naturally grounded on flowcharts is costly, thus FTD systems are impeded by scarce training data. To mitigate the data sparsity issue, we propose a plan-based data augmentation (PlanDA) approach that generates diverse synthetic dialog data at scale by transforming concise flowchart into dialogues. Specifically, its generative model employs a variational-base framework with a hierarchical planning strategy that includes global and local latent planning variables. Experiments on the FloDial dataset show that synthetic dialogue produced by PlanDA improves the performance of downstream tasks, including flowchart path retrieval and response generation, in particular on the Out-of-Flowchart settings. In addition, further analysis demonstrate the quality of synthetic data generated by PlanDA in paths that are covered by current sample dialogues and paths that are not covered.