Recently, edge artificial intelligence techniques (e.g., federated edge learning) are emerged to unleash the potential of big data from Internet of Things (IoT). By learning knowledge on local devices, data privacy-preserving and quality of service (QoS) are guaranteed. Nevertheless, the dilemma between the limited on-device battery capacities and the high energy demands in learning is not resolved. When the on-device battery is exhausted, the edge learning process will have to be interrupted. In this paper, we propose a novel Wirelessly Powered Edge intelliGence (WPEG) framework, which aims to achieve a stable, robust, and sustainable edge intelligence by energy harvesting (EH) methods. Firstly, we build a permissioned edge blockchain to secure the peer-to-peer (P2P) energy and knowledge sharing in our framework. To maximize edge intelligence efficiency, we then investigate the wirelessly-powered multi-agent edge learning model and design the optimal edge learning strategy. Moreover, by constructing a two-stage Stackelberg game, the underlying energy-knowledge trading incentive mechanisms are also proposed with the optimal economic incentives and power transmission strategies. Finally, simulation results show that our incentive strategies could optimize the utilities of both parties compared with classic schemes, and our optimal learning design could realize the optimal learning efficiency.