Integral field spectroscopy (IFS) of the central kiloparsecs of active galactic nuclei (AGNs) reveals a mixture of spatially coincident emission from star-formation and AGN feedback exciting the interstellar medium. Disentangling these components remains a challenge, as most spectral tracers are affected by both processes, limiting robust interpretation of kinematics and energetics. We present a new framework for decomposing IFS data into distinct components on a spaxel-by-spaxel basis using a multitracer, stacked kinematics approach. This method combines kinematic modelling with imposed flux decomposition per spaxel, quantifying the contribution of each component across the field of view. We apply this method to James Webb Space Telescope (JWST) IFS observations of the Seyfert galaxy NGC 5728 from the Galaxy Activity, Torus, and Outflow Survey, analysing twelve mid-infrared fine-structure lines ($4.49 \le \lambda \le 25.89 \,\mu$m, $7.9 \le$ IP $\le 126.2$ eV). We find that the circumnuclear emission can be decomposed into two dominant components: a star-forming ring and an AGN-driven biconical outflow. Our method separates these structures and recovers their detailed spatial morphology. This framework provides a general and scalable method for physically motivated component separation in IFS data, applicable across many wavelength ranges and targets, enabling reliable interpretation of complex emission line structures (or morphologies) in active galaxies and beyond.