The first demonstration of heterogeneous catalysis within an oscillatory baffled flow reactor (OBR) is reported, exemplified by the solid acid catalysed esterification of organic acids, an important prototypical reaction for fine chemicals and biofuel synthesis. Suspension of a PrSOH-SBA-15 catalyst powder is readily achieved within the OBR under an oscillatory flow, facilitating the continuous esterification of hexanoic acid. Excellent semi-quantitative agreement is obtained between OBR and conventional stirred batch reaction kinetics, demonstrating efficient mixing, and highlighting the potential of OBRs for continuous, heterogeneously catalysed liquid phase transformations. Kinetic analysis highlights acid chain length (i.e. steric factors) as a key predictor of activity. Continuous esterification offers improved ester yields compared with batch operation, due to the removal of water by-product from the catalyst, evidencing the versatility of the OBR for heterogeneous flow chemistry and potential role as a new clean catalytic technology.