We examined the effect of hydrogen (H2) enrichment on the primary fuel methane (CH4) in a canonical non-premixed bluff-body stabilized burner operating under typical central jet-dominated flame mode. In the chosen mode of operation, globally, the flow field and flame feature three important successive spatial zones: the recirculation zone, the neck zone, and the jet-like flame zone. The flame is exposed to a higher stretch rate in the neck zone in such a configuration and eventually undergoes local extinction. Such local extinction and subsequent re-ignition/reconnection of broken flame branches have substantial implications for the hydrodynamic instability of the coaxial annular air shear layer. It is well known that H2 addition increases the flame extinction strain rate ([Formula: see text] and thus alters the local extinction phenomenon. To understand this, we performed experiments at 0%, 10%, 20%, 30%, 50%, 80%, and 100% hydrogen proportion in the H2-CH4 blend. High repetition rate (5 kHz) Particle Image Velocimetry and OH Planar Laser Induced Fluorescence (PLIF) measurements are simultaneously implemented to gain quantitative insight into the flow field and flame structure. A detailed analysis performed over the instantaneous OH–PLIF datasets reveals the absence of local extinctions in flames with H2 enrichment >30% due to an increased extinction strain rate ([Formula: see text]. Furthermore, it is found that H2 enrichment plays a significant role in the reconnection/re-ignition of the broken flame branches formed during the local extinction. For instance, a high reconnection probability is observed in flames with an H2 addition of ≥20%. Consequently, variations in the mean reaction zone height are witnessed for different H2 enrichment levels. Further analysis of the influence of variation in reaction zone height on flow field hydrodynamics is explored using Proper Orthogonal Decomposition (POD) and Continuous Wavelet Transform (CWT). The results obtained from POD and CWT indicated the suppression of vortex shedding at the annular air shear layer for H2 addition greater than 20% and irregular wrinkling of flame fronts. Thus, they quantified the beneficial effect of H2 addition in turbulent flame stabilization.