Blockchain-based video streaming systems aim to build decentralized peer-to-peer networks with flexible monetization mechanisms for video streaming services. On these blockchain-based platforms, video transcoding, which is computational intensive and time consuming, is still a major challenge. Meanwhile, the block size of the underlying blockchain has significant impacts on the system performance. Therefore, this paper proposes a novel blockchain-based framework with adaptive block size for video streaming with mobile edge computing (MEC). First, we design an incentive mechanism to facilitate the collaborations among content creators, video transcoders and consumers. In addition, we present a block size adaptation scheme for blockchain-based video streaming. Moreover, we consider two offloading modes, i.e., offloading to the nearby MEC nodes or a group of device-to-device (D2D) users, to avoid the overload of MEC nodes. Then, we formulate the issues of resource allocation, scheduling of offloading, and adaptive block size as an optimization problem. We employ a low-complexity alternating direction method of multipliers (ADMM)-based algorithm to solve the problem in a distributed fashion. Simulation results are presented to show the effectiveness of the proposed scheme.