I wonder if there's any subtle meaning of the term? I find it redundant to include "density" since heat flux by definition is defined per unit area; the "density" sense is already implied. I of course refer to flux as vector quantity, not the scalar quantity as in calculus/electromagnetism.
A search in Google Scholar for "heat flux density" gives 17.4k hits, while ("heat flux" -density) gives 247k. Do certain disciplines have a special definition of the term or is it just a matter of lexical taste?