The challenge in the design of oxy-combustors for direct-fired supercritical CO2 (sCO2) cycles is in addressing disparate performance metrics and objectives. Key design parameters to consider include, among others, injector design for mixing and flame stability, split of recycled CO2 diluent between injectors and cooling films, target flame temperatures to control noncondensable products, and strategies to inject the diluent CO2 for film cooling and thermal control. In order to support novel oxy-combustor designs, a high-fidelity yet numerically efficient modeling framework based on the CRUNCH CFD® flow solver is presented, featuring key physics-based submodels relevant in this regime. For computational efficiency in modeling large kinetic sets, a flamelet/progress variable (FPV) based tabulated-chemistry approach is utilized featuring a three-stream extension to allow for the simulation of the CO2 film cooling stream in addition to the fuel and oxidizer streams. Finite rate chemistry effects are modeled in terms of multiple progress variables for the primary flame as well as for slower-evolving chemical species such as NOx and SOx contaminants. Real fluid effects are modeled using advanced equations of states. The predictive capabilities of this computationally tractable design support tool are demonstrated on a conceptual injector design for an oxy-combustor operating near 30 MPa. Simulations results provide quantitative feedback on the effectiveness of the film cooling as well as the level of contaminants (CO, NO, and N) in the exhaust due to impurities entering from the injectors. These results indicate that this framework would be a useful tool for refining and optimizing the oxy-combustor designs as well as risk mitigation analyses.