Operating stationary gas turbines on hydrogen-rich fuels offers a pathway to significantly reduce greenhouse gas emissions in the power generation sector. A key challenge in the design of lean-premixed burners, which are flexible in terms of the amount of hydrogen in the fuel across a wide range and still adhere to the required emission levels, is to prevent flame flashback. However, systematic investigations on flashback at gas turbine relevant conditions to support combustor development are sparse. The current work addresses the need for an improved understanding with an experimental study on boundary layer flashback in a generic swirl burner up to 7.5 bar and 300 °C preheat temperature. Methane-hydrogen-air flames with 50 to 85% hydrogen by volume were investigated. High-speed imaging was applied to reveal the flame propagation pathway during flashback events. Flashback limits are reported in terms of the equivalence ratio for a given pressure, preheat temperature, bulk flow velocity, and hydrogen content. The wall temperature of the center body along which the flame propagated during flashback events has been controlled by an oil heating/cooling system. This way, the effect any of the control parameters, e.g., pressure, had on the flashback limit was decoupled from the otherwise inherently associated change in heat load on the wall and thus change in wall temperature. The results show that the preheat temperature has a weaker effect on the flashback propensity than expected. Increasing the pressure from atmospheric conditions to 2.5 bar strongly increases the flashback risk, but hardly affects the flashback limit beyond 2.5 bar.