Privacy is an important facet of defence against adversaries. In this letter, we introduce the problem of private flocking. We consider a team of mobile robots flocking in the presence of an adversary, who is able to observe all robots' trajectories, and who is interested in identifying the leader. We present a method that generates private flocking controllers that hide the identity of the leader robot. Our approach towards privacy leverages a data-driven adversarial co-optimization scheme. We design a mechanism that optimizes flocking control parameters, such that leader inference is hindered. As the flocking performance improves, we successively train an adversarial discriminator that tries to infer the identity of the leader robot. To evaluate the performance of our co-optimization scheme, we investigate different classes of reference trajectories. Although it is reasonable to assume that there is an inherent trade-off between flocking performance and privacy, our results demonstrate that we are able to achieve high flocking performance and simultaneously reduce the risk of revealing the leader.