Boundary layer flashback of swirling turbulent lean-premixed methane–hydrogen–air flames is investigated in a model combustor featuring a mixing tube with center body. The focus of our work is on improving the understanding of the flow–flame interaction during flashback. We combine high-speed chemiluminescence imaging, stereoscopic and tomographic particle image velocimetry, and a three-dimensional flame front reconstruction technique to reveal the time-resolved, volumetric velocity field in the vicinity of the flame front during flashback. We find two different ways in which a flame front propagates upstream along the center body wall. The first mode concerns small-scale bulges counter-propagating into the approach flow, similar to channel-flow flashback, but is found not to be a dominant propagation mechanism. Instead, flashback occurs primarily in the form of large-scale flame tongues swirling in the bulk flow direction as they propagate upstream. The approach flow is modified significantly in both cases, but the scale and nature of the resulting velocity fields differ fundamentally. A key characteristic of the approach flow found previously, both in channel and swirl flame flashback, is regions of negative axial velocity upstream of the flame front. We reveal, however, that in the case of swirl flames the region of negative axial velocity is the result of a primarily swirling motion ahead of the leading flame tongue in contrast to the reverse flow pockets ahead of small-scale bulges. The boundary layer neither separates nor does fluid recirculate in the negative axial velocity region upstream of the flame tongues. Instead, flame tongues impose a local blockage effect causing significant deflection of the approach flow, which results in a constant region of negative axial velocity for the leading side of the flame tongue to propagate into.