The word flux comes from the way we talk about electromagnetism in Physics. Flux are imaginary lines that mediate E+M forces. We can see magnetic flux line by using iron filings, which form those lovely little parterns. The word flux density talks about the number of these lines passing through an area (density of them). Flux linkage is when a conducting material cuts through these lines, producing an EMF.
Flux density isn't really an old fashion word as we use the word flux alot more in degree level. Besides density always talks about something per unit something, ie 'density' is mass per unit volume, 'charge density' charge per unit volume. You could redefine flux density as how much line per unit volume (ie number of lines x average length / volume) its just that both the line length and the volume length is the same thing.