We summarize recent additions and improvements to the high energy density physics capabilities in FLASH, highlighting new non-ideal magneto-hydrodynamic (MHD) capabilities. We then describe 3D Cartesian and 2D cylindrical FLASH MHD simulations that have helped to design and analyze experiments conducted at the Vulcan laser facility. In these experiments, a laser illuminates a carbon rod target placed in a gas-filled chamber. A magnetic field diagnostic (called a Bdot) employing three very small induction coils is used to measure all three components of the magnetic field at a chosen point in space. The simulations have revealed that many fascinating physical processes occur in the experiments. These include megagauss magnetic fields generat...