A new method is presented for evaluating the performance of a nonlinear control allocation system within a linear control loop. To that end, a worst-case gain analysis problem is formulated that can be readily solved by means of well-established methods from robustness analysis using integral quadratic constraints (IQCs). It exploits the fact that control allocation systems are in general memoryless mappings that can be bounded by IQCs. A data-driven approach is used to find an optimal bound of the input/output mapping of the control allocation. Additionally, an iterative procedure based on local IQCs is introduced to determine meaningful sampling limits for less conservative yet accurate results.The effectiveness of the proposed data-driven performance analysis is shown at the example of an actively controlled flexible wing in a wind tunnel.