Multi-channel communication protocols have been developed to alleviate the effects of interference and consequently improve the network performance in Wireless Sensor Networks requiring high bandwidth. In this paper, we propose a contention-free multi-channel protocol to maximize network throughput while ensuring energy-efficient operation. Arguing that routing decisions influence to a large extent the network throughput, we formulate route selection and transmission scheduling as a joint problem and propose a Reinforcement Learning based scheduling algorithm to solve it in a distributed manner. The results of extensive simulation experiments show that the proposed solution not only provides a collision-free transmission schedule but also minimizes energy waste, which makes it appropriate for energy-constrained Wireless Sensor Networks.