For more than a decade, it has been observed that network traffic exhibits long-range dependence and many models have been proposed relating this property to heavy-tailed flow durations. However, none of these models consider correlations at flow scale. Such correlations exist and will become more prominent in the future Internet with the emergence of flow-aware control mechanisms correlating a flow's transmission to its characteristics (size, duration, etc.). In this work, we study the impact of the correlation between flow rates and durations on the long-range dependence of aggregate traffic. Our results extend those of existing models by showing that two possible regimes of long-range dependence exist at different time scales. The long-range dependence in each regime can be stronger or weaker than standard predictions, depending on the conditional statistics between the flow rates and durations. In the independent case, our proposed model consistently reduces to former approaches. The pertinence of our model is validated on real web traffic traces, and its ability to accurately explain the Hurst parameter is validated on both web traces and numerical simulations.