The lamellar-to-multilamellar vesicle (MLV) transformation in a model surfactant system, sodium dodecyl sulfate (SDS), octanol and brine, is investigated under continuous and oscillatory microfluidic contraction–expansion flows, employing polarised optical microscopy and small angle neutron scattering (SANS), with sample volume probed down to ≃20 nL. We determine the lamellar-to-MLV transition requirements at varying flow velocity, oscillation amplitude, frequency, and number of oscillatory cycles. The spatio-temporal evolution of the hierarchical fluid structure is elucidated: lamellar sheets initially align with flow direction upon entering a constriction and then perpendicularly upon exiting; the formation of MLVs at the nanoscale is first observed by SANS within a few (<5) oscillatory cycles, followed by the gradual appearance of a regular (albeit not crystalline) MLV arrangement, at the micronscale, by optical microscopy after tens of cycles, under the conditions investigated. Once MLVs form under flow, these remain metastable for several days.