Video steganography is the art of unobtrusively concealing secret data in a cover video and then recovering the secret data through a decoding protocol at the receiver end. Although several attempts have been made, most of them are limited to low-capacity and fixed steganography. To rectify these weaknesses, we propose a Large-capacity and Flexible Video Steganography Network (LF-VSN) in this paper. For large-capacity, we present a reversible pipeline to perform multiple videos hiding and recovering through a single invertible neural network (INN). Our method can hide/recover 7 secret videos in/from 1 cover video with promising performance. For flexibility, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos from the same cover video through specific keys. Moreover, we further improve the flexibility by proposing a scalable strategy in multiple videos hiding, which can hide variable numbers of secret videos in a cover video with a single model and a single training session. Extensive experiments demonstrate that with the significant improvement of the video steganography performance, our proposed LF-VSN has high security, large hiding capacity, and flexibility. The source code is available at https://github.com/MC-E/LF-VSN.