Recent trends such as automated driving in the automotive field and digitization in factory automation confront designers of real-time systems with new challenges. These challenges have arisen due to the increasing amount of data and an intensified interconnection of functions. For distributed safety-critical systems, this progression has the impact that the complexity of scheduling tasks with precedence constraints organized in so-called cause-effect chains increases the more data has to be exchanged between tasks and the more functions are involved. Especially when data has to be transmitted over an Ethernet-based communication network, the coordination between the tasks running on different end-devices and the network flows has to be ensured to meet strict end-to-end deadlines. In this work, we present an incremental heuristic approach that computes schedules for distributed and data-dependent cause-effect chains consisting of multi-rate tasks and network flows in time-sensitive networks. On the one hand, we provide a common task model for tasks and network flows. On the other hand, we introduce the concept of earliest and latest start times to speed up the solution discovery process and to discard infeasible solutions at an early stage. Our algorithm is able to solve large problems for synthetic network topologies with randomized data dependencies in a few seconds on average under strict end-to-end deadlines. We have achieved a high success rate for multi-rate cause-effect chains and an even better result for homogeneous or harmonic chains. Our approach also showed low jitter for homogeonous cause-effect chains.