How to convert theoretical template spectrum from luminosity density to flux density units?
Use this equation:
$$F_\nu = \frac{L_\nu}{4\pi D_L^2}.$$
This is the relationship that defines the luminosity distance, $D_L$, in a static Euclidean universe (i.e. not ours). Hogg has a good review on the arXiv of how to handle the relationship in an expanding universe, including when you need to perform something called a "$K$-correction" for spectral densities like the question asks.