The kandra, if they could mimic a tattoo , would have to alter the pigment in their own skin. Tattoo ink does not stay liquid in the skin, it cures and stains the skin and scar tissue.
The possiblity of mimicing a tattoo would depend greatly on what the tattoo actually is. As for the tattoos of an obligator or Inquisitor, if the mimic is possible it would be easy. The way they are discribed in the book, the ministry tattoos are tribal-like. This means they are lines or shapes that are filled in with color...usually black or red.
Now rendering a tattoo that contains a great amount of detail, may prove to be impossible...or at least take an excessive amount of time to reproduce. A tattoo is nothing more than a scar, but it's not like a scar from a normal wound. Tattoos that contain graduated shading, or really fine detail, would be exceptionally dificult to reproduce as the scars intertwine, leaving no definite pattern to mimic. It would probably turn out like a blob of muttled color.
As an expample...I actually have tribal flames tattooed on my right forearm. It would be easy to reproduce for a kandra, as it is solid black in the shape of flames. On the other hand, I have a tattoo on my left forearm, from wrist to elbow, that is full of minute details and lots of graduated shading. This would be more difficult to mimic as it blends colors and contains swirls...which means the lines in the scar itself are intertwined so there is no definite pattern to mimic.