The increasing product variance due to the growing individualization of customer requirements leads to smaller batch sizes and higher process time spreads in mixed-model assembly. The resulting decline in efficiency pushes conventional, less flexible assembly lines to the limits of their economic viability. Matrix assembly is an approach to increase flexibility and efficiency by decoupling workstations and dissolving cycle time constraints while maintaining flow. Both matrix and line assembly are flow-based assembly structures characterized by assembly objects moving according to the flow principle. Due to the numerous design options of flow-based assembly structures and the need to consider flexibility as a central decision criterion, the complexity of structural planning increases. The variety of the design options as well as their compatibility make it challenging for assembly planners to decide which configuration provides sufficient flexibility for their use case.This paper presents a novel level-based classification for flow-based assembly structures that identifies the relevant configurations, ranks them according to provided flexibility, and breaks down the characteristics as well as their compatibility. The classification enables planners to efficiently compile, evaluate and select the flow-based structure configurations suitable for the individual use case during assembly structure planning. Planning efficiency and results are improved by transparently providing all configurations and their characteristics' compatibility to the planner without any research effort. The configuration selection focusing on flexibility by means of the classification can be the starting point of a subsequent simulation of the system behavior concerning efficiency.