The blockchain technology has been extensively studied to enable distributed and tamper-proof data processing in federated learning (FL). Most existing blockchain assisted FL (BFL) frameworks have employed a third-party blockchain network to decentralize the model aggregation process. However, decentralized model aggregation is vulnerable to pooling and collusion attacks from the third-party blockchain network. Driven by this issue, we propose a novel BFL framework that features the integration of training and mining at the client side. To optimize the learning performance of FL, we propose to maximize the long-term time average (LTA) training data size under a constraint of LTA energy consumption. To this end, we formulate a joint optimization problem of training client selection and resource allocation (i.e., the transmit power and computation frequency at the client side), and solve the long-term mixed integer non-linear programming based on a Lyapunov technique. In particular, the proposed dynamic resource allocation and client scheduling (DRACS) algorithm can achieve a trade-off of [$\mathcal{O}(1/V)$, $\mathcal{O}(\sqrt{V})$] to balance the maximization of the LTA training data size and the minimization of the LTA energy consumption with a control parameter $V$. Our experimental results show that the proposed DRACS algorithm achieves better learning accuracy than benchmark client scheduling strategies with limited time or energy consumption.