Abstract High-precision measurements of flow coefficients $$v_{n}$$ v n ( $$n = 1 - 4$$ n = 1 - 4 ) for protons, deuterons and tritons relative to the first-order spectator plane have been performed in Au+Au collisions at $$\sqrt{s_{_{{\text {NN}}}= 2.4$$ s NN = 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 $$p_{{\text {t}}}$$ p t and rapidity $$y_{{\text {cm}}}$$ 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 $$v_{1}$$ v 1 , $$d v_{1}/d y^{\prime }|_{y^{\prime } = 0}$$ d v 1 / d y ′ | y ′ = 0 where $$y^{\prime }$$ y ′ is the scaled rapidity, and for $$v_{2}$$ v 2 at mid-rapidity. Scaling with the number of nucleons is observed for the $$p_{{\text {t}}}$$ p t  dependence of $$v_{2}$$ v 2 and $$v_{4}$$ v 4 at mid-rapidity, which is indicative for nuclear coalescence as the main process responsible for light nuclei formation. $$v_{2}$$ v 2 is found to scale with the initial eccentricity $$\langle \epsilon _{2} \rangle $$ ⟨ ϵ 2 ⟩ , while $$v_{4}$$ v 4 scales with $$\langle \epsilon _{2} \rangle ^{2}$$ ⟨ ϵ 2 ⟩ 2 and $$\langle \epsilon _{4} \rangle $$ ⟨ ϵ 4 ⟩ . The multi-differential high-precision data on $$v_{1}$$ v 1 , $$v_{2}$$ v 2 , $$v_{3}$$ v 3 , and $$v_{4}$$ v 4 provides important constraints on the equation-of-state of compressed baryonic matter.