For the latest GOFS 3.1 Analysis
from Dec-04-2018 to Present we have the net heat flux "qtot" in the "sur" dataset:
However, we don't have this for the GOFS 3.1 Reanalysis.
HYCOM uses a bulk parameterization, based on model SST and input atmospheric fields, to calculate the latent and sensible heat flux. So it isn't practical to calculate the GOFS Reanalysis net heat flux from the CFSR and CFSv2 datasets. The short and long wave are from the "downwelling" CFSR fields, with albedo giving the net shortwave and upwelling longwave from model SST.
We don't have a way to subset CFSR for download, but it isn't going to be much use to you in any case.
Alan.