In advanced gas turbine engines, high-pressure combustion generally occurs with combustion chamber pressure exceeding the critical pressure of the engine fuel. In this paper, large eddy simulations are conducted in a dual swirl gas turbine model combustor to analyze the effects of different fuel-air equivalence ratios and chamber pressures on swirling injection and turbulent combustion. Numerical results reveal that intricate interactions exist between swirling flows and high-pressure turbulent flame. Strong swirling injection of air could cause reverse flows in the inner injector, which lead to a V shaped partially premixed turbulent flame at a chamber pressure of 3 MPa. As the operating pressure increases to 5 MPa, decreased injection velocity would prevent reverse flows in the inner injector, leading to the turbulent diffusive flame. On the other hand, combustion causes flow acceleration, gaseous expansion, and strong thermophysical property variations, which would influence the reverse flows, increase the expansion angle in swirling injection, and dictate the size of central recirculation zone and the oscillation frequency of precessing vortex core. Results obtained herein would help gain fundamental understanding on high-pressure swirling flows and flame dynamics in advanced gas turbine engines.