How to input the amplification factor for wave induced velocity in CAESER II?

Please provide more details on this question.

Have you reviewed the "hydrodynamic input" dialog?

If the riser is located near jacket leg, the wave velocity and current should be multiplied by an amplification factor. For current, we can input it by selecting user defined option. But for wave induced velocity, how to account for the amplication factor effect in CAESER II?

You can't. The wave equations are solved and the resulting particle velocities and accelerations are computed, and used. If current is also defined, it is vectorially added to the wave partical veocities.

How woud you quantify this increase factor?

With refer to code DNV-OS-F101 section E 300, the increase factor is computed as:-
1+(R^2/z^2)
Where:
R = cylinder radius
z = distance between cylinder centre and actual location (z>=R)