I cannot work out what you did wrong :no: - so I did it again, it is much quicker like that ;), here it is:
Papper-box.blend (496 KB)
Just press PLAY to see it working. To enhance the display I have added a Solidify Modifier to the mesh so the “paper” has some thickness. I remade the mesh and the armature, use XYZ Euler rotation for the bones in this instance I think, and parented the mesh to the armature “With Empty Groups” then just assigned the flaps to their respective bones, there is no need to assign any vertices to the lid bone since the flaps bones are parented to it.
Hope this helps you and say hello the the “Vasa” for me next time you pass that way. I shall be in Stockholm and Sundsvall at the end of July/ early August.