The purposes of this study were to provide a game-based anti-phishing lesson to 110 elementary school students in Taiwan, explore their learning behavioral patterns, and investigate the effects of the flow states on their learning behavioral patterns and learning achievement. The study recorded behaviour logs, and applied a pre- and post-test on phishing knowledge and a flow state measurement to analyze the learning process. The study used lag sequential analysis to infer the students' behavioural patterns. The results showed that the learning materials used in this study can enable learners' flow experience, whereby they can acquire anti-phishing knowledge through trial and error via a repeated "learning with gaming" behavioral pattern. We recommend that future educators and researchers on this topic appropriately increase the level of difficulty of the games used, and design learning materials with flexible difficulty based on learners' flow states.