The characteristics of isenthalpic planar premixed flames in counterflowing, high Reynolds number streams with counter‐ and corotating swirl are analyzed by activation energy asymptotics for a one‐step Arrhenius reaction with small departures from unity Lewis numbers. Density changes resulting from heat release are fully taken into account. For moderate rates of rotation, the situation considered in the present study, there is only one stagnation plane that is coincident with the plane of symmetry separating the inviscid outer flows and that involves a viscous layer with an embedded flame in some circumstances. The analysis of a flame in the viscous layer is relevant to the experimentally observed variation of the lean flammability limit with the rotation rate. Comparison with the existing experimental data is carried out.