In this work, the study of an innovative chaotic system made from two memristors with symmetric bifurcation and multistability is presented. Within a four dimensional chaotic framework, the system is architected with two flux controlled memristors. Computational simulations reveal intricate dynamical phenomena such as symmetric bifurcations, multistability, and very large sensitivity to initial conditions. Using Lyapunov exponents, bifurcation diagrams and phase portraits, we investigate the system's ability to produce chaotic attractors of pronounced multistability. Pinched hysteresis loop and system offset investigation at different frequencies are investigated for possible applications in neuromorphic computing, random number generation and secure communication protocols. We further advance our understanding of the complex dynamical properties of memristive chaotic systems. A representative analog circuit corroborates their numerical findings.