Hashing has been widely adopted for large-scale data retrieval in many domains due to its low storage cost and high retrieval speed. Existing cross-modal hashing methods optimistically assume that the correspondence between training samples across modalities is readily available. This assumption is unrealistic in practical applications. In addition, existing methods generally require the same number of samples across different modalities, which restricts their flexibility. We propose a flexible cross-modal hashing approach (FlexCMH) to learn effective hashing codes from weakly paired data, whose correspondence across modalities is partially (or even totally) unknown. FlexCMH first introduces a clustering-based matching strategy to explore the structure of each cluster and, thus, to find the potential correspondence between clusters (and samples therein) across modalities. To reduce the impact of an incomplete correspondence, it jointly optimizes the potential correspondence, the cross-modal hashing functions derived from the correspondence, and a hashing quantitative loss in a unified objective function. An alternative optimization technique is also proposed to coordinate the correspondence and hash functions and reinforce the reciprocal effects of the two objectives. Experiments on public multimodal data sets show that FlexCMH achieves significantly better results than state-of-the-art methods, and it, indeed, offers a high degree of flexibility for practical cross-modal hashing tasks.