  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 $^{87}$Rb 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 interplay of the staggered flux and flat-band
localization under the mechanism of Aharonov-Bohm caging. 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 topologically protected by the winding of the Floquet Bloch bands
of a coarse-grained effective Hamiltonian. The observed chiral transport offers
a strategy for efficient quantum device design where topological robustness is
ensured by fast Floquet driving and flat-band localization.
