Much attention has focused on the transmon architecture for large-scale superconducting quantum devices; however, the fluxonium qubit has emerged as a possible successor. With a shunting inductor in parallel to a Josephson junction, the fluxonium offers larger anharmonicity and stronger protection against dielectric loss, leading to higher coherence times as compared to conventional transmon qubits. The interplay between the inductive and Josephson energy potentials of the fluxonium qubit leads to a rich dispersive-shift landscape when tuning the external flux. Here, we propose to exploit the features in the dispersive shift to improve qubit readout. Specifically, we report on theoretical simulations showing improved readout times and error rates by performing the readout at a flux-bias point with large dispersive shift. We expand the scheme to include different error channels and show that with an integration time of 155 ns, flux-pulse-assisted readout offers about a 5-times improvement in the signal-to-noise ratio. Moreover, we show that the performance improvement persists in the presence of finite measurement efficiency combined with quasistatic flux noise and also when considering the increased Purcell rate at the flux-pulse-assisted readout point. We suggest a set of reasonable energy parameters for the fluxonium architecture that will allow for the implementation of our proposed flux-pulse-assisted readout scheme.