This paper introduces the multiscale coherent reaction front (MSRC) model, a predictive framework for the analysis of hydrodynamic and thermoacoustic instabilities in co-flow fuel-air burners. The MSRC model integrates nonlinear Ginzburg-Landau dynamics with acoustic coupling and large eddy simulation (LES). Model validation with experimental burner data from the University of Alberta (including flame structure, temperature, species concentration, velocity and vorticity fluctuations, and pollutant emissions) has been performed and confirms its accuracy. The MSRC framework captures complex transitions from stable combustion to limited cyclic oscillations (LCO) and chaotic behavior. Analysis of velocity and vorticity fluctuations reveals low-frequency (<200 Hz) coherent structures in the nozzle that correlate with the acoustic modes of the system and confirm shear layer instability. The model also distinguishes high-frequency shear layer instabilities (at high Reynolds numbers) from thermoacoustic coupling. Finally, it is shown that optimization of the aligned airflow can stabilize combustion and reduce pollutant emissions. These results provide a valuable tool for the design of stable and low-emission combustion systems.