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We examine multiple disjointness of minimal flows, that is, we find conditions under which the product of a collection of minimal flows is itself minimal. Our main theorem states that, for a collection ${X_i}_{i\in I}$ of minimal flows with a common phase group, assuming each flow satisfies certain structural and algebraic conditions, the product ${\prod }_{i\in I}{X}_i$ is minimal if and only if ${\prod }_{i\in I}{X}_i^{eq}$ is minimal, where $X_i^{eq}$ is the maximal equicontinuous factor of $X_i$. Most importantly, this result holds when each $X_i$ is distal. When the phase...