The H2-hybridization of premixed methane-air flames stabilized above perforated plates is hindered by the flashback tendency of hydrogen-rich flames. This study investigates the role of flame quenching by heat losses to the burner wall on flashback mechanisms. A set of canonical multi-perforated plates with various sub-millimeter slit widths is studied experimentally. Depending on the slit width and operating conditions, two regimes of hydrodynamic flashback initiation are identified. The first is solely controlled by the kinematic imbalance between flow and flame speed downstream of the flame-holder. The second is governed by the ratio of the slit width over a quenching distance that depends on the temperature of the preheated reactants. A method that allows to determine the quenching width at any preheat temperature for a given plate geometry and operating condition is presented. This approach enables to differentiate the two hydrodynamic flashback regimes. A map of flame stabilization and flashback regimes depending on the slit width and H2-hybridization rate is proposed based on the experiments. The controlling mechanisms leading to a specific regime of flashback for a given operating condition are unveiled. Flame quenching is found to inhibit the influence of the Lewis number on flashback limits in narrow slits. This prevents the abrupt increase in the ratio of bulk flow velocity to laminar flame speed at flashback, a phenomenon observed in larger slits when the effective Lewis number falls below Le = 0.5. These results establish the role of quenching in flashback phenomena and may support the design of hydrogen-robust multi-perforated burners.