Deep learning (DL) based channel state information (CSI) feedback in multiple-input multiple-output (MIMO) systems recently has attracted lots of attention from both academia and industrial. From a practical point of views, it is huge burden to train, transfer and deploy a DL model for each parameter configuration of the base station (BS). In this paper, we propose a scalable and flexible framework for DL based CSI feedback referred as scalable CsiNet (SCsiNet) to adapt a family of configured parameters such as feedback payloads, MIMO channel ranks, antenna numbers. To reduce model size and training complexity, the core block with pre-processing and post-processing in SCsiNet is reused among different parameter configurations as much as possible which is totally different from configuration-orienting design. The preprocessing and post-processing are trainable neural network layers introduced for matching input/output dimensions and probability distributions. The proposed SCsiNet is evaluated by metrics of squared generalized cosine similarity (SGCS) and user throughput (UPT) in system level simulations. Compared to existing schemes (configuration-orienting DL schemes and 3GPP Rel-16 Type-II codebook based schemes), the proposed scheme can significantly reduce mode size and achieve 2%-10% UPT improvement for all parameter configurations.