This paper presents the development and application of high-fidelity neutronic models of the SPARC tokamak for the design of neutron flux monitors (NFM) for application during plasma operations. NFMs measure the neutron flux in the tokamak hall, which is related to fusion power via calibration. We have explored Boron-10 gamma-compensated ionization chambers (ICs) and parallel-plate Uranium-238 fission chambers (FCs). We plan for all NFMs to be located by the wall in the tokamak hall and directly exposed to neutrons streaming through a shielded opening in a midplane port. Our simulations primarily use a constructive solid geometry-based OpenMC model based on the true SPARC geometry. The OpenMC model is benchmarked against a detailed CAD-based MCNP6 model. The B10 ICs are equipped with high-density polyethylene (HDPE) sleeves, borated HDPE housings, and borated aluminum covers to shield out scattered neutrons, optimize detector response levels, and make calibration robust against changes in the tokamak hall. The B10 neutron absorption branching ratio may cause the detectors’ responses to be non-linear to neutron flux >200 keV. However, our simulations unveil that, in the SPARC environment and with the proposed housings and sleeves, >99% of the detector responses are induced by <100 keV neutrons. U238’s insensitivity to slow neutrons makes this FC a promising candidate for direct fusion neutron measurements. Along with a borated HDPE sleeve, about 60% of the FCs’ responses are induced by direct neutrons.