The current study presents a numerical investigation of the flow field of a swirl-stabilized burner featuring a non-swirling axial air jet on the central axis of the mixing tube. The system has been designed and optimized to burn hydrogen at the Technische Universität Berlin over the last 6 years in the context of the EU-funded projects GREENEST and AHEAD. As the burner design was based on experimental work, high-fidelity large-eddy simulations (LES) are used to provide deeper understanding on the non-reacting and reacting flow fields to elucidate the occurrence of flashback under certain operating conditions. The experimental measurements suggest that flashback is produced by a velocity deficit at the mixing tube outlet and these conditions are analyzed here using LES. The work includes code validation for non-reacting and reacting conditions by comparison to water tunnel and combustion test rig data, and aims to evaluate the accuracy of LES with a combustion model based on premixed flamelets to predict the reacting flow field under conditions close to flashback.