Fluid–structure interaction (FSI) problems involving free-surface flows and elastic bodies remain a significant challenge in computational mechanics due to their complex coupling behavior, large interface deformations, and high computational demands. To address these challenges, this study proposes a high-efficiency, fully coupled numerical framework that integrates flexible plate models based on the Absolute Nodal Coordinate Formulation (ANCF) with an Immersed Boundary–Lattice Boltzmann Flux Solver (IB–LBFS). The proposed approach enables accurate simulation of both free-surface flow dynamics and the nonlinear response of elastic structures undergoing large deformations. In the fluid domain, the IB–LBFS method combines the mesoscopic lattice Boltzmann scheme with macroscopic flux reconstruction, along with a volume-force-based immersed boundary technique. An implicit boundary correction strategy is introduced to enforce no-slip conditions, while computational efficiency is enhanced through sparse matrix compression and a conjugate gradient iterative solver for velocity correction. For the structural domain, a four-node ANCF shell element with 48 degrees of freedom is employed, allowing accurate representation of large rigid–flexible motion without the need for coordinate transformations, thereby ensuring stable and precise structural dynamics analysis. The framework is validated through a dam-break scenario involving impact on an elastic vertical barrier. The simulation results show strong agreement with benchmark solutions obtained from space–time finite element and particle finite element methods. The method effectively captures free-surface evolution, structural modal behavior, and detailed pressure and displacement histories. Furthermore, compared to conventional space–time finite element approaches, the proposed solver achieves approximately a 33.3% reduction in computational time per FSI step under equivalent mesh conditions.