The effect of magnetic flux on nonlinear dc transport through a chaotic 2D quantum dots and Aharonov-Bohm rings is investigated. Generally non-linear conductance is asymmetric function of applied field, and its anti-symmetric component in particular is very sensitive to presence of Coulomb interaction. The sample-to-sample fluctuationsof the nonlinear conductance are found for arbitrary temperature, magnetic field, and interaction strength. Unlike the Aharonov-Bohm oscillations in linear trasport through the rings, where the phase is pinned to 0 or $\pi$, the phase of AB-oscillations in nonlinear conductance fluctuates. We investigate statistics of phase and amplitude of oscillations and make comparison with recent experiments.