The relationship between specific discharge and flux
I assume you are talking about the fluid dynamics description of flux, which is the rate of volume flow across a unit area.

1. 


  Is flux simply specific discharge × area?


Yes you are correct.

$$Specific~Discharge = \frac{Volumetric~Flux}{Area}$$

therefore

$$Volumetric~Flux = Specific~Discharge~\cdot~Area$$

2. 


  And when we speak of flux of an element eg. N-flux, is that specific
  discharge × concentration × area?


When you speak of an element the rationale is the same but will depend on whether the model you are devising contains 1D, 2D or 3D fluid elements. The latter is defined as above.