Learning 3D+t shape completion and generation from multi-view cardiac magnetic resonance (CMR) images requires a large amount of high-resolution 3D whole-heart segmentations (WHS) to capture shape priors. In this work, we leverage flow matching techniques to learn deep generative flows for augmentation, completion, and generation of 3D+t shapes of four cardiac chambers represented implicitly by segmentations. Firstly, we introduce a latent rectified flow to generate 3D cardiac shapes for data augmentation, learned from a limited number of 3D WHS data. Then, a label completion network is trained on both real and synthetic data to reconstruct 3D+t shapes from sparse multi-view CMR segmentations. Lastly, we propose CardiacFlow, a novel one-step generative flow model for efficient 3D+t four-chamber cardiac shape generation, conditioned on the periodic Gaussian kernel encoding of time frames. The experiments on the WHS datasets demonstrate that flow-based data augmentation reduces geometric errors by 16% in 3D shape completion. The evaluation on the UK Biobank dataset validates that CardiacFlow achieves superior generation quality and periodic consistency compared to existing baselines. The code of CardiacFlow is released publicly at https://github.com/m-qiang/CardiacFlow .