The popularity of wearable cameras has opened up a new dimension for egocentric activity recognition. While some methods introduce attention mechanisms into deep learning networks to capture fine-grained hand-object interactions, they often neglect exploring the spatio-temporal relationships. Generating spatial attention, without adequately exploiting temporal consistency, will result in potentially sub-optimal performance in the video-based task. In this paper, we propose a flow-guided spatial attention tracking (F-SAT) module, which is based on enhancing motion patterns and inter-frame information, to highlight the discriminative features from regions of interest across a video sequence. A new form of input, namely the optical-flow volume, is presented to provide informative cues from moving parts for spatial attention tracking. The proposed F-SAT module is deployed to a two-branch-based deep architecture, which fuses complementary information for egocentric activity recognition. Experimental results on three egocentric activity benchmarks show that the proposed method achieves state-of-the-art performance.