Your analogy of flattening the cube into six two dimensional squares is appropriate, but, unfortunately, simplistic.
The pseudodragon model is made up of not one, but thirteen separate objects, head/neck, body, tail, two-part wings x2, legs x2, feet x2, arms x2 (the body, legs x2 and arms x2 may actually be one object, but I doubt it).
Each of these objects are irregularly shaped, consisting of many irregular faces (triangles). Flattening out each of these objects would require some of the triangles to be "unhitched" from adjacent triangles by spitting the shared vertice between the two triangles. This would allow each triangle to be rotated out of its plane to the "flat" plane.
For example, if you consider a simple
icosahedron (also known to us PnP folk as the d20), you can see how a
three dimensional object is made from a
two dimensional shape consisting of twenty equilateral triangles.
As you can imagine, for irregularly shaped faces (triangles), this is a
non-trival task. I am not aware of any software tool that would do this.
Further, in computers, such "objects" can overlap in space, creating the illusion of a single flexible object.
However, in physical space, these objects would no longer be able to overlap, and you would have to cut parts out of them so that they could come together.
Hope this helps.
Regards,
Script Wrecked.