Amorphous glassy materials of diverse nature -- concentrated emulsions, granular materials, pastes, molecular glasses -- display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications. A classical feature, well documented yet not really understood, is the very non-linear nature of the flow rule relating stresses and strain rates. Using a microfluidic velocimetry technique, we characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughness. Beyond the classical non-linearities of the rheological behaviour, we evidence finite size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast, a rather simple non-local flow rule is shown to account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of the cooperativity of the flow at these scales, that is unobservable in the liquid state (lower concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers, e.g. coatings, our assessment of non-locality and cooperativity echoes observations on other glassy, jammed and granular systems, suggesting a possible fundamental universality.
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