We report on the observation of flexoelectricity of an asymmetric "swallow-tail" compound by dissolving it in a BMAOB nematic matrix and studying the thickness dependence of the period of longitudinal (2nd order) domains in planar layers under d.c. excitation. From the experimental data and Bobilev-Pikin theory we estimate the value of the flexocoefficient difference \e*\ = \e(\z) - e(3x)\ as a function of the evaluation about expected concentration and evaluate an extrapolated value of this difference for the "swallow-tail" compound.