Mobile crowdsensing (MCS) counting on the mobility of massive workers helps the requestor accomplish various sensing tasks with more flexibility and lower cost. However, for the conventional MCS, the large consumption of communication resources for raw data transmission and high requirements on data storage and computing capability hinder potential requestors with limited resources from using MCS. To facilitate the widespread application of MCS, we propose a novel MCS learning framework leveraging on blockchain technology and the new concept of edge intelligence based on federated learning (FL), which involves four major entities, including requestors, blockchain, edge servers and mobile devices as workers. Even though there exist several studies on blockchain-based MCS and blockchain-based FL, they cannot solve the essential challenges of MCS with respect to accommodating resource-constrained requestors or deal with the privacy concerns brought by the involvement of requestors and workers in the learning process. To fill the gaps, four main procedures, i.e., task publication, data sensing and submission, learning to return final results, and payment settlement and allocation, are designed to address major challenges brought by both internal and external threats, such as malicious edge servers and dishonest requestors. Specifically, a mechanism design based data submission rule is proposed to guarantee the data privacy of mobile devices being truthfully preserved at edge servers; consortium blockchain based FL is elaborated to secure the distributed learning process; and a cooperation-enforcing control strategy is devised to elicit full payment from the requestor. Extensive simulations are carried out to evaluate the performance of our designed schemes.