The only way I know how to do that would be to create a mesh with the subUV layout and use render to texture.
So if you want a 256^3 volume, you need 256 slices stacked one atop another with the right spacing, and they need to be laid out in UV space in a 16x16 fashion. Then you can do render to texture and capture your material that way.
Or you could render out the individual frame slices and use an external program to stitch them into a flipbook.
I haven’t actually done it but it should work. I am trying to do all my volume stuff in UE4.
This type of stuff should get easier once true 3d texture support is in the engine. But I am not sure what that pipeline will look like either.