Electrohydrodynamic (EHD) flows are known to cause rigid colloids to aggregate near electrodes. Here we report that EHD flows also induce immiscible oil droplets to aggregate and, for sufficiently strong field strengths, to coalesce. We measure the aggregation and coalescence rates of micrometer-scale oil droplets in water, and we find that the most effective way to induce coalescence is by suddenly decreasing the applied frequency. We interpret the results in terms of a balance between EHD flow and colloidal forces, and we discuss the implications for using El-ID flows to separate trace oils from solution.