If you are inquiring about Darcy Flux then it is the same thing as a Darcy Velocity (units of length/time or cubic length/(cubic area x time)...both are the same). From Darcy's Law, it is the hydraulic conductivity (or K) multiplied by the hydraulic gradient (dh/dL), i.e., the drop in hydraulic head in the direction and distance of travel.
If you are asking about mass flux (units of mass/(Area x time)), as defined in Physics, then you have to multiply by the water density somewhere. Here are some simple links:
https://www.groundwatersoftware.com/page39.html
https://www.enviro.wiki/index.php?title=Mass_Flux_and_Mass_Discharge
Note that the second link is about contaminant flux in groundwater.
The water flux is defined as the product of inundation depth, width of the channel and depth-averaged current velocity.
V= KI/n. In this formula V stands for "groundwater velocity," K equals the "horizontal hydraulic conductivity," I is the "horizontal hydraulic gradient," and n is the "effective
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