Chaotic circuits have been demonstrated as a potential avenue for improving system reliability with respect to computation and memory capacity when compared to those that depend on the methodical behavior of components. In this work, we demonstrate how flux-coupled memristive pairs influence the chaotic dynamics of Chua's circuit. An analog emulator circuit is built to model an idealized flux-controlled memristor, and compositely connected to an identical circuit to simulate flux-coupling. Our circuit is then implemented in Chua's circuit to characterize the influence of flux-coupling on chaotic oscillations. We mathematically model the behavior of the system in MATLAB, and verify its operation in PSpice, and thus characterize the periodic and chaotic states caused by varying the coupling strength. Therefore, we successfully demonstrate the ability for natural phenomena to be capable of modulating chaotic oscillations without the need for control circuitry.