This paper models and analyzes international trade flows using open flow networks (OFNs) with the approaches of flow distances, which provide a novel perspective and effective tools for the study of international trade. We discuss the establishment of OFNs of international trade from two coupled viewpoints: the viewpoint of trading commodity flow and that of money flow. Based on the novel model with flow distance approaches, meaningful insights are gained. First, by introducing the concepts of trade trophic levels and niches, countries' roles and positions in the global supply chains (or value-added chains) can be evaluated quantitatively. We find that the distributions of trading "trophic levels" have the similar clustering pattern for different types of commodities, and summarize some regularities between money flow and commodity flow viewpoints. Second, we find that active and competitive countries trade a wide spectrum of products, while inactive and underdeveloped countries trade a limited variety of products. Besides, some abnormal countries import many types of goods, which the vast majority of countries do not need to import. Third, harmonic node centrality is proposed and we find the phenomenon of centrality stratification. All the results illustrate the usefulness of the model of OFNs with its network approaches for investigating international trade flows.