A lab-scale bluff body combustor is mapped for its stability and flame dynamics of non-premixed flames. The characteristics are observed across variations in the fuel composition, as well as in the inlet flow rate. The combustor is seen to exhibit markedly different dynamics for each of the varied fuel compositions. This behavior is explained on the basis of mean flame stabilization behavior and on the combined effects of the fuel-jet momentum flux and global equivalence ratio. It is seen that the H2 flames primarily act as a pilot source for secondary combustion of either CO or CH4. Further, it is seen that, the high momentum flux associated with H2-CO mixtures result in combustion near the wall and outside the bluff-body shear layers at low inlet flow rates. Whereas, at high inlet flow rates, the mean heat release rate is seen to stabilize closer to the injection holes as well as extend to near the bluff-body shear layer. This marked difference in flame stabilization is seen to have a drastic effect on the nature of oscillations inside the chamber. This is contrasted to H2-CH4 (synthesis natural gas) flames that exhibit stabilization inside the bluff-body wake at high inlet flow rate. The difference between H2-CH4 and H2-CO flames with regards to combustion dynamics is then explained as a result of the flame stabilization behavior, which is seen to be different across the varied fuel compositions. While H2-CH4 flame exhibits the well-known large wake structures responsible for combustion instability, H2-CO flame exhibits no such structures, owing to their stabilization point. Further analysis using pressure fixed phase instants reveal the difference in nature of combustion dynamics across the tested fuel compositions and are justified using the spatial Rayleigh index map.