High-precision measurements of flow coefficients v_n (n= 1 - 4) for protons, deuterons and tritons relative to the first-order spectator plane have been performed in Au+Au collisions at sNN=2.4 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at the SIS18/GSI. Flow coefficients are studied as a function of transverse momentum p_t and rapidity y_cm over a large region of phase-space and for several classes of collision centrality. A clear mass hierarchy, as expected by relativistic hydrodynamics, is found for the slope of v₁, dv1/dy′|y′=0 where y^′ is the scaled rapidity, and for v₂ at mid-rapidity. Scaling with the number of nucleons is observed for the p_t dependence of v₂ and v₄ at mid-rapidity, which is indicative for nuclear coalescence as the main process responsible for light nuclei formation. v₂ is found to scale with the initial eccentricity ⟨ ϵ₂⟩ , while v₄ scales with ⟨ϵ2⟩2 and ⟨ ϵ₄⟩. The multi-differential high-precision data on v₁, v₂, v₃, and v₄ provides important constraints on the equation-of-state of compressed baryonic matter.