Prior multi-frame optical flow methods typically estimate flow repeatedly in a pair-wise manner, leading to significant computational redundancy. To mitigate this, we implement a Streamlined In-batch Multi-frame (SIM) pipeline, specifically tailored to video inputs to minimize redundant calculations. It enables the simultaneous prediction of successive unidirectional flows in a single forward pass, boosting processing speed by 44.43% and reaching efficiencies on par with two-frame networks. Moreover, we investigate various spatiotemporal modeling methods for optical flow estimation within this pipeline. Notably, we propose a simple yet highly effective parameter-efficient Integrative spatiotemporal Coherence (ISC) modeling method, alongside a lightweight Global Temporal Regressor (GTR) to harness temporal cues. The proposed ISC and GTR bring powerful spatiotemporal modeling capabilities and significantly enhance accuracy, including in occluded areas, while adding modest computations to the SIM pipeline. Compared to the baseline, our approach, StreamFlow, achieves performance enhancements of 15.45% and 11.37% on the Sintel clean and final test sets respectively, with gains of 15.53% and 10.77% on occluded regions and only a 1.11% rise in latency. Furthermore, StreamFlow exhibits state-of-the-art cross-dataset testing results on Sintel and KITTI, demonstrating its robust cross-domain generalization capabilities. The code is available here.