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Kagome antiferromagnet is one of the most studied models for geometrical frustration which is expected to be a topological magnon insulator in the presence of Dzyaloshinskii–Moriya interactions. The recent discovered tripod kagome materials provide us a platform to explore such ideas with strongly spin-orbit coupled rare earth ions. Using elastic neutron scattering measurements, we show that one of the tripod kagome compounds, Yb₃Mg₂Sb₃O₁₄, orders into a strongly non-coplanar magnetic ground state below 0.88 K which calls for large antisymmetric exchanges. Inelastic neutron scattering experiment on polycrystalline samples reveals both dispersive and flat magnon bands which can be fitted by an anisotropic exchange Hamiltonian derived from a symmetry analysis. Along with numerical calculations, our results unveil Yb₃Mg₂Sb₃O₁₄ as a candidate to host topological non-trivial magnon bands.