The mixing of fuel and air is a key factor in determining NOx emissions during combustion. Lean-premixed burning strategies allow to control the flame temperature and therefore NOx emissions. However, for highly reactive fuels like hydrogen, the high flame speed makes full premixing dangerous due to the increased risk of flashback. In these cases, current combustor geometries are often operated in partially premixed modes with the fuel injected as close as possible to the combustion chamber. This highlights the need for effective mixing strategies to achieve a high degree of mixing over a short distance. This is even more critical in fuel-flexible combustion systems (e.g., combustors capable of burning both CH4 and H2), as the mixing process is heavily influenced by the varying properties of the fuel mixture. In such cases, a comprehensive understanding of the mixing process is required to minimize NOx emissions under all fuel blends conditions. This paper investigates the mixing of fuel jets into a swirling air cross-flow of a partially-premixed, swirl stabilized combustor using a combined experimental and numerical approach. The injector features an axial swirler and a mixing tube where the air and the fuel jets mix before entering the combustion chamber. The experiments are performed in cold flow conditions. A variable mixture of helium–air is used to represent different blends of CH4-H2 fuel, and the mixing process is visualized by seeding the fuel stream with DEHS droplets. Large-Eddy Simulations (LES) confirm the suitability of helium as a surrogate for H2 by demonstrating similar macro-mixing behavior for the two gases. This study examines the impact of varying fuel composition and momentum flux ratio (Jswirl) between the fuel jet and the swirling cross-flow on mixing performance. The results indicate that fuel with lower density achieve better mixing with the air at the mixing tube outlet. A numerical analysis of the radial transport terms reveals that higher H2 content in the fuel makes it less subject to outward convection which causes stratification close to the mixing tube outlet. Furthermore, the contribution of the molecular diffusion term increases with higher levels of H2, resulting in improved mixing. When increasing Jswirl (up to Jswirl = 10) increases the penetration of the fuel jet into the swirling flow. Above a critical value of Jswirl, the mixture homogeneity at the mixing tube outlet becomes insensitive to Jswirl for the investigated geometry. Overall, the fuel composition was found to have a greater influence on the level of mixing close to the mixing tube outlet than variations in Jswirl.