How to use spectral flux density data while using Planck's law giving spectral radiance?
As I understand it, spectral flux is defined as
$ F_{\nu} = \int_\Omega I_{\nu}(\theta, \phi)\cos{\theta} d\Omega $
where $d\Omega$ is the solid angle element over which the integral is performed. Here $I_{\nu}$ is the specific intensity. The $\nu$ subscript denotes frequency dependence.
According to A. Choudhuri &quot;Astrophysics for Physicists&quot; p. 25, blackbody sources are isotropic emitters therefore we can drop the angular dependence in the spectral intensity and $I_{\nu}(\theta, \phi)$ becomes your Planck formula $B_{\nu}(T)$.
Hence
$ F_{\nu} = \pi B_{\nu}(T)$