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Aeroelasticity simulations increase in importance for aircraft design, requiring an efficient coupling of computational fluid dynamics (CFD) with computational structure mechanics (CSM) solvers. This contribution investigates the scalability of a high-fidelity CFD-CSM toolchain on modern high-performance computing (HPC) architectures. It consists of DLR's TAU solver for fluid dynamics simulations [1], and FlowSimulator [2] components for the incorporation of precomputed structural normal mode data, as well as for the underlying mesh deformations. The computational performance of the entire simulation pipeline is evaluated using a single measurement suite, allowing to identify bottlenecks of individual components and differences in their scalability. Preliminary improvements are realized via hybrid parallelization. Although this study focuses on a specific toolchain, key findings about scalability issues are relevant for complex CFD-CSM or other coupled simulations in general.