A

Let's denote the swimmer's speed in still water as \( S \) and the speed of the river as \( R \).
From the problem, we have:
1. Swimming with the current: \( S + R = 16 \) km/h
2. Swimming against the current: \( S - R = 8 \) km/h

Now, we can solve these two equations simultaneously:

Adding the two equations:
\( (S + R) + (S - R) = 16 + 8 \)
\( 2S = 24 \)
\( S = 12 \) km/h (swimmer's speed in still water)

Now, substituting \( S \) back into one of the original equations to find \( R \):
\( 12 + R = 16 \)
\( R = 16 - 12 \)
\( R = 4 \) km/h (velocity of the flow of the river)

Therefore, the swimmer's speed in still water is 12 km/h and the velocity of flow of the river is 4 km/h.