<p>The manipulation of particle transport in synthetic quantum matter is an active research frontier for its theoretical importance and potential applications. Here we experimentally demonstrate an engineered topological transport in a synthetic flat-band lattice of ultracold ⁸⁷Rb atoms. We implement a quasi-one-dimensional rhombic chain with staggered flux in the momentum space of the atomic condensate and observe biased local oscillations that originate from the flat-band localization under the staggered synthetic flux. Based on these features, we design and experimentally confirm a state-dependent chiral transport under the periodic modulation of the synthetic flux. We show that the phenomenon is associated with the topology of the Floquet Bloch bands of a coarse-grained effective Hamiltonian. Our work opens the new avenue for exploring flat-band-assistant topological transport with ultracold atoms, and offers a new strategy for designing efficient quantum device with topological robustness.</p><p></p>