Time-sensitive networking (TSN) can help standardize deterministic Ethernet across industrial automation. The deterministic guarantee of TSN is based on network resource scheduling in the unit of flow. However, the state-of-the-art TSN single flow scheduling scheme cannot meet the coordinated scheduling requirements of multiple data flows in advanced industrial applications (e.g., control and safety applications). In this article, we propose a TSN chain flow abstraction, TC-Flow, for a coordinated multiple-flow scheduling model in industrial control and safety applications. Based on the proposed TC-Flow model, we design an offline TC-Flow scheduling algorithm using integer linear programming and an online heuristic TC-Flow scheduling algorithm to handle network dynamics. To deploy the proposed TC-Flow model and scheduling algorithms in the TSN, we design a CF-TSN network architecture that is compatible with the existing TSN single-flow scheduling scheme. Finally, we implement the proposed CF-TSN architecture and TC-Flow scheduling algorithms in real-world network environments. Experimental results show that the proposed scheduling algorithms can increase the number of schedulable flows by 26 percent compared to the state-of-the-art TSN scheduling benchmark.