Computer-Supported Collaborative Learning (CSCL) is recognized as an effective methodology for fostering social interaction mediated by technology in ways that potentially trigger learning. The successful implementation of CSCL hinges on factors such as the scripting mechanics for activity sequencing proposed by Collaborative Learning Flow Patterns (CLFP). Yet, research in CSCL scripts has not studied if CLFPs achieves the so-called notion of "flow experience," defined as an optimal state in which individuals are engaged and absorbed in an activity. This study proposes an approach to measure flow in the case of the Pyramid CLFP and studies the factors that influence the flow experience in the PyramidApp tool. The study tests a model that uses analysis of the Flow Short Scale and data logs. The findings show that there is a relationship between factors such as the speed of individual contributions and active participation in groups with the flow experience. Notably, the quantity of participation does not exhibit a discernible impact on the flow. The study emphasizes the interest of the modelled factors and the proposed approach for learning analytics to understand the flow experience in CLFP implementations.