Flood disasters are among the most frequent and impactful natural disasters globally, causing significant economic losses and human casualties. Accurate prediction of emergency material demand is crucial for improving rescue efficiency and minimizing losses. However, the "small sample and insufficient information" nature of flood data restricts forecasting accuracy. To address this, we propose an improved GM(1,1) dynamic forecasting model for predicting affected populations based on grey system theory. A dynamic emergency material demand model is further developed by integrating inventory management theory and predicted population data. The model was validated using a flood disaster case in Jiangxi Province, China, in June 2024. Results showed that: (1) The improved GM(1,1) model demonstrated high prediction accuracy, with the precision test Mean squared Error Ratio (MSER, c = 0.27) and Small Error Probability (SEP, p = 1) both meeting Grade I standards, making it suitable for forecasting affected populations; (2) Case analysis showed that the improved GM(1,1) model outperformed the traditional GM(1,1) model in terms of MSER (c = 0.22<0.31) and SEP (p = 1.0>0.92), with predicted values closer to actual values; (3) The dynamic demand model estimated material requirements from June 24 to July 6, including 15.48 million liters of drinking water, 14,700 tons of food, 8,700 tons of medicine, 2.9 million tents, 10.95 million quilts, and 29,000 signal stations.This study improves dynamic flood response by enabling emergency relief demand prediction and supporting deployments in civil engineering and disaster prevention, including resettlement planning, levee inspections, and identification of key transport nodes.