The layered compound KCu\(_3\)As\(_2\)O\(_7\)(OD)\(_3\), comprising distorted kagome planes of \(S=1/2\) Cu\(^{2+}\) ions, is a recent addition to the family of type-II multiferroics. Previous zero field neutron diffraction work has found two helically ordered regimes in \kns, each showing a distinct coupling between the magnetic and ferroelectric order parameters. Here, we extend this work to magnetic fields up to \(20\)~T using neutron powder diffraction, capacitance, polarization, and high-field magnetization measurements, hence determining the \(H-T\) phase diagram. We find metamagnetic transitions in both low temperatures phases around \(\mu_0 H_c \sim 3.7\)~T, which neutron powder diffraction reveals to correspond to a rotation of the helix plane away from the easy plane, as well as a small change in the propagation vector. Furthermore, we show that the sign of the ferroelectric polarization is reversible in a magnetic field, although no change is observed (or expected on the basis of the magnetic structure) due to the transition at \(3.7\)~T. We finally justify the temperature dependence of the polarization in both zero-field ordered phases by a symmetry analysis of the free energy expansion.