The standard transforms in Fuse support 3D transformation, but you need to have a 3D viewport enabled first. At the root of your app (sorry, it’s not supported elsewhere yet) add:
<Viewport Perspective="100"> ... your app ... </Viewport>
Where Perspective is the distance to the camera. There is also a CullFace="Back" option that will cause things to not draw when facing backwards, but you should instead make them invisible insted. Culled objects are still there and will receive pointer events, potentially blocking other input.
Then you rotate things in 3D in an action, such as <Rotate DegreesY="45"/>.
There are also the TransformOrigin="HorizontalBoxCenter" and VerticalBoxCenter to assist in such transforms. These set the rotation point of an object such that it was the face of a box of that size. In the particular card animation you are showing however this is probably not needed.
As you said still have to hide it and display the other, will tackle that right away :).
I had to set the perspective to Perspective="1000" so the card looks inside the panel when rotating, on the preview it seems that it flickers a bit BUT in the phone looks just fine.