Molecular docking that predicts the bound structures of small molecules (ligands) to their protein targets, plays a vital role in drug discovery. However, existing docking methods often face limitations: they either overlook crucial structural changes by assuming protein rigidity or suffer from low computational efficiency due to their reliance on generative models for structure sampling. To address these challenges, we propose FABFlex, a fast and accurate regression-based multi-task learning model designed for realistic blind flexible docking scenarios, where proteins exhibit flexibility and binding pocket sites are unknown (blind). Specifically, FABFlex's architecture comprises three specialized modules working in concert: (1) A pocket prediction module that identifies potential binding sites, addressing the challenges inherent in blind docking scenarios. (2) A ligand docking module that predicts the bound (holo) structures of ligands from their unbound (apo) states. (3) A pocket docking module that forecasts the holo structures of protein pockets from their apo conformations. Notably, FABFlex incorporates an iterative update mechanism that serves as a conduit between the ligand and pocket docking modules, enabling continuous structural refinements. This approach effectively integrates the three subtasks of blind flexible docking-pocket identification, ligand conformation prediction, and protein flexibility modeling-into a unified, coherent framework. Extensive experiments on public benchmark datasets demonstrate that FABFlex not only achieves superior effectiveness in predicting accurate binding modes but also exhibits a significant speed advantage (208 $\times$) compared to existing state-of-the-art methods. Our code is released at https://github.com/tmlr-group/FABFlex.