Grasping large flat objects, such as books or keyboards lying horizontally, presents significant challenges for single-arm robotic systems, often requiring extra actions like pushing objects against walls or moving them to the edge of a surface to facilitate grasping. In contrast, dual-arm manipulation, inspired by human dexterity, offers a more refined solution by directly coordinating both arms to lift and grasp the object without the need for complex repositioning. In this paper, we propose a model-free deep reinforcement learning (DRL) framework to enable dual-arm coordination for grasping large flat objects. We utilize a large-scale grasp pose detection model as a backbone to extract high-dimensional features from input images, which are then used as the state representation in a reinforcement learning (RL) model. A CNN-based Proximal Policy Optimization (PPO) algorithm with shared Actor-Critic layers is employed to learn coordinated dual-arm grasp actions. The system is trained and tested in Isaac Gym and deployed to real robots. Experimental results demonstrate that our policy can effectively grasp large flat objects without requiring additional maneuvers. Furthermore, the policy exhibits strong generalization capabilities, successfully handling unseen objects. Importantly, it can be directly transferred to real robots without fine-tuning, consistently outperforming baseline methods.