The Ising model-in which degrees of freedom (spins) are binary valued (up/down)-is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy$3$Mg$2$Sb$3$O$\mathrm{<mrow\; data-mjx-texclass="ORD">14</mrow>}$ hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ~0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy$3$Mg$2$Sb$3$O$\mathrm{<mrow\; data-mjx-texclass="ORD">14</mrow>}$ as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.