Data-driven deep learning has been utilized to provide fast yet accurate predictions for the multi-phase flow systems, thus significantly accelerating the downstream tasks like design and optimization. However, the performance of data-driven deep learning heavily relies on the amount of available data. In order to tackle the scenario with limited data, this paper develops a spatio-temporal transfer learning framework, named TransReactorNet, for predicting unsteady multi-phase flow fields in the coal-supercritical water fluidized bed reactor. Besides, this framework presents a coordinate affine transformation technique to address the issue of handling 3D unstructured flow data. Furthermore, an efficient residual modeling strategy built upon pure 3D convolutional neural networks with the direct multi-step forecasting and the channel independent strategy is developed to capture spatio-temporal multi-phase flow characteristics. Comprehensive comparison study against the competitors indicates that the TransReactorNet model can provide accurate and fast prediction of the unsteady multi-phase flow fields with scarce data. By leveraging knowledge transfer from the spatio-temporal data of reactors with similar operational conditions, the proposed method achieved remarkable performance metrics, attaining a peak-signal-to-noise ratio exceeding 35 dB and a structural similarity index above 0.96, while requiring only 10% of the target training data. Besides, it showcases good generalizability and low time complexity, indicated by the approximately 20x GPU memory consumption reduction compared to counterparts, and the nearly 1500x speedup compared to the numerical solver.