Currently enums can not be in a cluster that you want convert to JSON. It would be great, if this could be added.
Either the enum value could be converted to its internal representation (e.g. u16) or the value could be saved as a string (make it easier to read the JSON and parse it outside LabVIEW).
The unflatten should be able to handle the u16 easily to convert back to enum or take the string and search through the enum of the datatype that one has to connect to the vi. If there is no match the VI can issue an error.