Immersed Boundary Methods (IBM) are extensively used to model effect of solid geometries in incompressible fluid-flow simulations. A Lagrangian markers-based formulation in particular offers great flexibility during simulation of fluid-structure interaction problems, which involve moving geometries on a block-structured Adaptive Mesh Refinement (AMR) grid. A flavor of this formulation based on a Moving Least-Squared (MLS) approach has been implemented in FLASH for solution of single-phase incompressible Navier-Stokes equations. FLASH is the predecessor of Flash-X, a Multiphysics scientific software instrument, which leverages AMR libraries like Paramesh and AMReX for grid management and implements its particle infrastructure natively to support applications ranging from astrophysics to multiphase fluid dynamics . In this work, we will address the growing need to leverage immersed boundaries as a generalized approach for treating effect of complex solid geometries in Flash-X by extending MLS to implement a ghost fluid type approach for explicitly enforcing normal gradients of physical quantities at solid-fluid interface. This strategy enables solution of conjugate flux problems that occur during heat transfer and chemical adsorption. We will implement this formulation using Flash-X’s particle infrastructure to effectively distribute and manage Lagrangian markers representing solid bodies as they move through the computational domain and quantify performance of our algorithm.