Many studies have investigated how interpersonal differences between users influence their experience in Virtual Reality (VR) and it is now well recognized that user's subjective experiences and responses to the same VR environment can vary widely. In this study, we focus on player traits, which correspond to users' preferences for game mechanics, arguing that players react differently when experiencing VR scenarios. We developed three scenarios in the same VR environment that rely on different game mechanics, and evaluate the influence of the scenarios, the player traits and the time of practice of the VR environment on users' perceived flow. Our results show that 1) the type of scenario has an impact on specific dimensions of flow; 2) the scenarios have different effects on flow depending on the order they are performed, the flow preconditions being stronger when performed at last; 3) almost all dimensions of flow are influenced by the player traits, these influences depending on the scenario, 4) the Aesthetic trait has the most influences in the three scenarios. We finally discuss the findings and limitations of the present study that we believe have strong implications for the design of scenarios in VR experiences.