Synthetic biomimetic prototissues with reduced complexity can facilitate the understanding of intricate biological processes, by allowing the role of specific physical or chemical mechanisms to be isolated. The aim of the present work is to provide a rheological description of vesicle prototissues as a biomimetic model for the flow of cellular tissues, which can be relevant for the mechanical comprehension of embryogenesis or tumor metastasis. Prototissue were obtained by the controlled assembly of Giant Unilamellar Vesicles (GUVs) mediated by the biotin-streptavidin pair, using a simple assembly protocol. Prototissues were mechanically probed in a “pipette-aspiration” inspired microfluidic chip, under controlled pressure conditions. A viscoelastic flow behavior was obtained which was well captured by a generalized Kelvin-Voigt fluid model, with inferred rheological parameters that did not show a significant dependence on the GUV-GUV adhesion strength. In addition, the flow of the vesicle prototissues exhibited a strain-stiffening behavior. Complementary flow velocimetry analysis revealed a decrease of prototissue effective permeability with the applied pressure, and enabled to identify vesicle spatial reorganizations taking place within the prototissue. Overall, our microfluidic setup makes possible the simultaneous characterization of the biomimetic prototissue at two different length scales, global and local, bridging the viscoelastic response of the overall prototissue with its structural changes between an ensemble of vesicles.