Mobility analysis is an important step in the conceptual design of flexure systems. It involves identifying directions with unrestricted motion (freedoms) and directions with restricted motion (constraints). This paper proposes a deterministic framework for mobility analysis of wire flexure systems by characterizing a kinetostatic vector field known as "load flow" through its geometry. The relationship between load flow and the flexure axis is used to determine if a flexure behaves as a constraint or a freedom. This knowledge is utilized to formulate a matrix-based reduction technique to determine flexure mobility in an automated fashion. Several examples with varying complexity are illustrated to validate the efficacy of this technique. This technique is particularly useful in analyzing complex hybrid interconnected flexure topologies, which may be non-intuitive or involved with traditional methods. The proposed framework combines both visual insight and analytical rigor, and will complement existing analysis and synthesis techniques.