Virtual flow metering (VFM) is a cost-effective and non-intrusive technology for inferring multi-phase flow rates in petroleum assets. Inferences about flow rates are fundamental to decision support systems which operators extensively rely on. Data-driven VFM, where mechanistic models are replaced with machine learning models, has recently gained attention due to its promise of lower maintenance costs. While excellent performance in small sample studies have been reported in the literature, there is still considerable doubt towards the robustness of data-driven VFM. In this paper we propose a new multi-task learning (MTL) architecture for data-driven VFM. Our method differs from previous methods in that it enables learning across oil and gas wells. We study the method by modeling 55 wells from four petroleum assets. Our findings show that MTL improves robustness over single task methods, without sacrificing performance. MTL yields a 25-50% error reduction on average for the assets where single task architectures are struggling.