Abstract This article presents a numerical study of a jet-in-hot-coflow (JHC) burner which emulates Moderate or Intense Low-oxygen Dilution (MILD) conditions. Such combustion regime offers reduction in pollutant emissions and improvements in efficiency. However, some phenomena like the relations between auto-ignition and flame propagation, local extinction and re-ignition are not easily detected by experimental analysis or through the inspection of CFD calculations. The advanced post-processing tools based on the theories of computational singular perturbation (CSP) and tangential stretching rate (TSR) are adopted to investigate the Large Eddy Simulation (LES) results of the JHC burner with different coflow oxygen levels. A topological characterization of the flowfield is achieved employing the local number of chemically exhausted modes, highlighting regions that share similar dynamical features. Strong chemical activity, denoted by a small number of exhausted modes, is found in the fuel/coflow mixing layer and, to a minor extent, in the coflow/air mixing layer, exhibiting correlation with the higher heat release rate zones. The analysis of the reactive layers with TSR suggests that the flame under MILD condition is initiated by auto-ignition. Moreover, the investigation of the TSR participation indices (PIs) mark the local extinction and re-ignition zone for the low oxygen level case, indicating that the lack of oxygen in the coflow suppresses the path to produce final combustion products and heat—thus reducing the reactivity of the whole system.