Linked meshes are meant to use with skins.
A linked mesh due to runtime performance can only work if kept in the same slot.
Therefore the correct way to use a linked mesh is to create your mesh, turn it in a linked mesh and then move the generated child in a different skin/keep it as alternative image of the parent mesh.
To change the image double click on the child and change path/name. It will of course only show either as an alternative to the current image in the same skin, or in a different skin.