To investigate the dynamics of complex combustion processes in highly turbulent flows, the analysis of data from elaborate measurements or simulations is necessary. In this study the machine learning-based algorithm of cluster-based network modeling is applied to an extensive experimental data-set of a bistable swirl-stabilized flame, which alternates between a V- and an M-shape regime. The method is used to efficiently build a low-order representation of the flame and flow dynamics which consists of representative flow states, identified from snapshot clusters and transition probabilities between them. The identified model is found to accurately reproduce the main characteristics of both flame regimes. The precessing vortex core (PVC) encountered during the M-flame is mapped to strong periodic transitions within the corresponding cluster domain. The V-shaped flame is found to exhibits a more stochastic behavior. Furthermore, the identified low-order model gives insight to the transition mechanism between the two regimes. The validation of the network using a second dataset at equal operating conditions demonstrates its generalizability. The approach is found to be promising for data-driven low-order modeling of highly complex dynamics.