Understanding the connection between shallow subsurface magmatism and related surface expressions provides first-order insight into the volcanic and tectonic processes that shape a planet's evolution. When assessing the role of flexure, previous investigations assumed homogeneous host rock, but planetary lithospheres typically include crust and mantle material, and the mechanical response of a layered lithosphere subjected to flexure may influence both shallow magma reservoir failure and intrusion propagation. To assess the formation of giant radial dike systems, such as those observed on Venus, we create axisymmetric elastic finite element models of a spherical reservoir centered at the contact between stiff, dense mantle overlain by softer, lighter crust. We analyze magma chamber stability, overpressure at rupture, and resulting intrusion types for three distinct environments: lithostatic, upward flexure, and downward flexure. In the lithostatic case, reservoir failure at the crust-mantle contact favors lateral sill injection. In the flexure cases, we observe that failure location depends upon the crust/lithosphere thickness ratio and, at times, will favor radial dike intrusion. Specifically, upward flexure can promote the formation of giant radiating dike swarms, a scenario consistent with a plume-derived origin. Our results present a mechanical explanation for giant radial dike swarm formation, showing that both the stability of magma chambers on Venus and the type of intrusions that form are influenced by lithospheric layering. Furthermore, where dike swarms occur, our approach provides a powerful new way to constrain local crust/mantle layering characteristics within the lithosphere at the time the swarm was forming.