The magma flow into the eruption site of Geldingadalir does not show any trace of origin in the form of subduction. Therefore, no magma chamber is visible. The magma ascends directly from the mantle. The path can be traced according to the convection rolls model and a simplified drawing of the basic structure of the tectonic plate.
What is confusing is the interplay between convection rolls of the two uppermost layers. The layer interacting directly with the tectonic plate extends from the Reykjanes Ridge (and the Kolbeinsey Ridge as well). Magma ascends from the division line into the ductile part of tectonic plate, until it reaches the brittle part (or the crust itself). Usually, backflow of Munroe Effect would take all the magma back to the lower circulation process. What can happen, is that the lower convection rolls get coupled with the upper one, leading to tension, and thereby opening paths from below, enabling magma to flow horizontally below the brittle crust. The crust has been extended for a long period of time due to the effect of the uppermost roll of the area, opposing the main drift direction of the North American Tectonic Plate.
It has also been pointed out by Vigfús Eyjólfsson, that the eruption site is found where the dike crosses an earthquake fault of the area, creating the weakness within the crust for enabling lava to flow on the surface.