Understanding the complex connection between flow-processing history, fluid structure, and fluid properties represents a grand challenge for the engineering and fundamental study of nanostructured soft materials. To address this challenge, we report measurements using scanning small-angle x-ray scattering in a fluidic four-roll mill (FFoRM), which enables rapid nanostructural characterization of complex fluids under an unprecedentedly diverse range of flow histories. Combining this technique with analysis of the Lagrangian deformation history of fluid elements, we demonstrate rapid mapping of orientational ordering of fluids' nanostructure along diverse deformation trajectories that emulate those encountered in flow processing. Using demonstrative experiments on model rodlike nanoparticle dispersions, we show that differences in rod flexibility and rod-rod interactions play a significant role in determining the fluid's anisotropic structural response to similar flow histories. An analysis of the coupling between measured particle alignment and interparticle correlations reveals these differences to arise from the nature and strength of interparticle interactions in flow. These measurement and analysis techniques produce large datasets that hold promise toward advancing process-structure-property models and inverse design processes of flows that are tailored to produce targeted nanostructures.