The integration of artificial intelligence (AI) in healthcare, powered by Internet of Medical Things (IoMT) data, offers significant potential for personalized and efficient patient care. Hierarchical federated learning (HFL) is a promising approach for healthcare applications, combining cross-silo and cross-device federated learning. This architecture allows hospitals to train local models using patient data, while sharing anonymized parameters with other hospitals to improve diagnosis. However, existing studies on incentive mechanisms in HFL often focus on determining optimal incentive values but neglect the integration of these incentives into the reward stage. Moreover, the two-layer architecture of HFL introduces challenges related to disparities in patient volume and diversity across hospitals. In this paper, we propose a fair incentive distribution mechanism for hierarchical systems using blockchain state channels. We ensure equal incentive budget contributions from all organizations, preventing free-riders in the HFL system with a channel factory solution. Additionally, virtual channels support transactions without intermediaries, minimizing computational costs in the blockchain network.