Brain effective connectivity (EC) is key to understanding causal neural interactions and brain organization. However, learning EC from single-modal brain data, such as functional magnetic resonance imaging (fMRI) or electroencephalography (EEG), is limited by the inability to simultaneously capture sparse temporal and spatial information. This paper proposes a novel multimodal sparse generative flow network (MSGFlowNet), which integrates fMRI and EEG data through an attention-guided encoder and employs a multi-head self-attention sparse Transformer to extract features from the fused data. These features are then processed by two output heads of the generative flow network: one computes state transition probabilities and updates the mask, while the other determines the probability of generating a termination state. Experiments on synthetic and real-world datasets demonstrate that MSGFlowNet significantly outperforms state-of-the-art methods.