Electron doped rhombohedral multilayer graphene at high displacement field features an exceptionally flat band minimum with near-ideal quantum geometry. Experiments in this regime observe the formation of a 'quarter metal,' in which the electron liquid condenses into a single spin- and valley flavor. Remarkably, recent experiments have found a zero resistance state in the same region of the density- and displacement-field-tuned parameter space, attributed to the formation of a chiral superconductor characterized by a finite-momentum Cooper pair condensate. Here, we use nanoSQUID-on-tip magnetometry to map the orbital magnetization of electron-doped rhombohedral graphene devices ranging in thickness between 3 and 13 layers. Magnetization within the quarter metal phases peaks at finite density, consistent with concentration of the Berry curvature in a finite-momentum 'ring of fire'. Correlating transport and local magnetometry data in a tetralayer sample reveals that the superconducting state has a finite orbital magnetic moment, providing direct evidence of its chiral nature. We further show that widely observed stochastic switching of the resistivity in the metallic regime arises from a density-tuned sign change in the valley-resolved total magnetic moment. This leads to the formation of metastable magnetic domains under typical gate control sequences and can also be harnessed for electric-field controlled switching of orbital moment across the entire device. Unexpectedly, we find magnetic inhomogeneity specific to the apparent normal state of the chiral superconductor, suggestive of a strain-tuned competition between magnetic and non-magnetic ground states. Our results point to a subtle energetic competition underlying the observation of chiral superconductivity in a narrow range of layer numbers.