Data flow systems allow the user to design a flow diagram that specifies the relations between system components which process, filter or visually present the data. Visualization systems may benefit from user-defined data flows as an analysis typically consists of rendering multiple plots on demand and performing different types of interactive queries across coordinated views. In this paper, we propose VisFlow, a web-based visualization framework for tabular data that employs a specific type of data flow model called the subset flow model. VisFlow focuses on interactive queries within the data flow, overcoming the limitation of interactivity from past computational data flow systems. In particular, VisFlow applies embedded visualizations and supports interactive selections, brushing and linking within a visualization-oriented data flow. The model requires all data transmitted by the flow to be a data item subset (i.e. groups of table rows) of some original input table, so that rendering properties can be assigned to the subset unambiguously for tracking and comparison. VisFlow features the analysis flexibility of a flow diagram, and at the same time reduces the diagram complexity and improves usability. We demonstrate the capability of VisFlow on two case studies with domain experts on real-world datasets showing that VisFlow is capable of accomplishing a considerable set of visualization and analysis tasks. The VisFlow system is available as open source on GitHub.