LabVIEW has built-in VIs that work to manipulate 1D and even 2D arrays, but there isn't anything that helps with a 3D array. The reason for this is because you can use the built-in functions to manipulate a 3D array. This example shows the work needed in order to use those built-in functions to Transpose a 3D Array. This VI is polymorphic, so it will work with Doubles, Booleans or Strings as shown below.

As you can see, the Transpose 3D array allows you to Transpose each of the different dimensions. This subVI can also be cascaded to accomplish more advanced transposing.