High-fidelity computational fluid dynamics (CFD) remains computationally expensive for steady aerodynamic prediction under multi-condition and variable-geometry configurations, which limits rapid design iteration. To address this issue, this study proposes a data-driven surrogate framework for aircraft surface flow-field prediction on irregular meshes. The framework combines a geometry-unification strategy for variable rudder-deflection configurations with KM-GAT, a hybrid neural architecture that integrates graph attention and KAN-based nonlinear feature transformation. Geometry unification maps the surface flow fields associated with different rudder-deflection states onto a common zero-deflection reference template, thereby establishing consistent mesh correspondence and fixed prediction locations across samples while retaining the rudder angle as an operating-condition variable. The KM-GAT model further combines topology-aware message passing with localized nonlinear refinement, while the Huber loss is adopted to improve training robustness for CFD-derived data. Experiments on the F-22 research model show that the proposed framework achieves lower prediction errors and more concentrated error distributions than baseline MLP and GNN-based models. Qualitative comparisons further indicate that KM-GAT better preserves localized high-gradient structures, including pressure transitions and vortex-dominated regions. These results suggest that the proposed framework provides an effective surrogate modeling strategy for variable-geometry aerodynamic flow field prediction.