How do I import an animated FBX mesh that does not have a skeleton / armature (Plants/Trees)?

Right, the only way to translate your animation from Blender to UE4 is to convert it to vertex animation, what that means is that it contains keyframe keys for each vertex of the mesh so it doesn’t depend on any skeleton rig or any special animation tools in your 3D software, it would take any animation and convert it to simple position animation for each vertex. However, you understand it’s very inefficient which is why I suggest getting that wind sway animation in your material which would can shift the positions of the vertices to create a wind swaying animation in the trees. This is something that many games do for things like grass and trees. I believe that Speedtree does something like that too.