The AdS/CFT correspondence provides an equivalence between a gravity theory in some bulk anti-deSitter spacetime and a conformal field theory (CFT) in one fewer dimensions on the boundary. A superconductor that can be described by a gravity theory through this correspondence is referred to as a 'holographic superconductor'. Gradient flow equations will evolve any given initial field configuration towards one that is a solution to the equations of motion, this allows us to study stability of solutions as well as the behavior of a system far from equilibrium. Through the AdS/CFT correspondence, the gradient flow in the gravity theory should have a corresponding flow in the CFT and vice-versa. We focus on the flow of the matter fields in a gravity theory containing a black hole and a charged scalar field. In this system the flow equations move the system from a configuration with no scalar hair to a hairy black hole solution. We study the corresponding flow on the boundary superconducting theory, where a normal metal state transitions to a superconducting state.