Bremsstrahlung radiation emitted by runaway electrons is one of the most widely used diagnostic signals in tokamak plasmas. In this contribution, we present a bremsstrahlung radiation transport workflow based on the general-purpose Monte Carlo code FLUKA and apply it to the modeling of bremsstrahlung transport within the COMPASS tokamak facility. The model includes the generation of bremsstrahlung radiation, which is essential for the definition of the source term in the Monte Carlo simulation, its transport through the tokamak environment, and the response of a selected detector. The obtained results are validated against measurements performed during a runaway electron campaign at the COMPASS tokamak, and the main simplifications of the modeling workflow are discussed. The developed approach provides a framework for the interpretation of experimental data and for the optimization of bremsstrahlung diagnostics in current and future tokamak experiments, including the COMPASS Upgrade tokamak.