Isolated stellar-mass black holes (IBHs) are expected to be abundant in the Milky Way, yet their electromagnetic signatures remain largely undetected. We investigate the detectability of IBHs in molecular clouds using a 1D, multi-wavelength emission model that incorporates magnetic flux transport controlled by the magnetic Prandtl number Pₘ. We find that magnetically arrested disks (MADs) form for Pₘ≳ 1, where the magnetic flux threading the black hole is in a saturation value. On the other hand, MAD formation is restricted to a limited parameter range for Pₘ<1, In our model, outer parts of accretion disks, around 100 gravitational radii, efficiently emit infrared photons detectable by WISE. This feature is not captured by the conventional one-zone model. X-ray emission depends strongly on Pₘ; For Pₘ=1 where MAD is formed, X-ray emission is dominated by nonthermal radiation, whereas inverse Compton emission becomes dominant for Pₘ=0.5 where the magnetic field is weaker than the saturation value. X-ray detection is plausible if they are in dense molecular-cloud filaments for Pₘ≥1, although it is challenging for Pₘ< 1. These results demonstrate that magnetic flux transport plays a key role in shaping the multiwavelength observational signatures of IBHs.