The present article investigates the correlation between flame macrostructures and thermoacoustic combustion instabilities in stratified swirling flames. Experiments are carried out in a laboratory scale longitudinal test rig equipped with the Beihang Axial Swirler Independently-Stratified (BASIS) burner, a novel double-swirled combustion system developed by adapting an industrial lean premixed prevaporized (LPP) combustor. At first, the flame macrostructures are investigated and discussed for various total equivalence ratios (ϕtotal) and stratification ratios (SRs). Depending on operating conditions, three different flame types are stabilized in the combustor: two attached flames comprising a stratified flame and a V-shaped flame (V-flame), as well as a lifted flame. Thermoacoustic instabilities are then investigated. The amplitude of the oscillations is found to be more sensitive to SR than the ϕtotal. Large amplitude limit cycles are found for low and high values of SR, for which the V-flame and the lifted flame are observed in the combustor, respectively. The flame dynamics are also investigated using local Rayleigh index maps. It is found that for both the lifted flame and V-flame, the major driving force comes from the flame-to-wall impingement region. Coherent structures associated with flame wrinkling are found along the flame brushes of the V-flame. On the contrary, the stratified flame is found to be more thermo-acoustically stable. Finally, incompressible Large Eddy Simulations is used to obtain the flame responses to forcing at 300 Hz, which is very close to the frequencies at which limit cycle oscillations occur. The results show that the global heat release rate response of the stratified flame exhibits a significant phase shift compared to the responses of the other two flame types, and this is the most likely cause of thermoacoustic stabilization.