Basaltic fissure eruptions, the most common type of eruption on Earth, are fed by dykes, which are magma-filled cracks that propagate through the crust. It is well-established that dykes have a segmented structure, but the impact of this structural complexity on the development of magma flow pathways and on the behaviour of any subsequent eruptions remains largely unexplored. Here, we present field evidence from a solidified dyke in Tenerife (Canary Islands, Spain) that is exceptionally well-exposed, displaying segmentation structures that reveal complex, three-dimensional magma transport pathways. The dyke consists of plate-like lobes, and its layered internal textures record flow localisation, analogous to lava tube development in pahoehoe flow fields. We propose that flow localisation mediates magma supply to the leading edge of the propagating dyke, creating a convoluted plumbing system that likely influences eruption behaviour, and which should be accounted for in models of magma transport.