I would confirm the ability to not parallel flexible conductors with the crane manufacturer and/or the energy chain manufacturer. I believe they are the only ones that can give an opinion on their listed equipment.
On a side note, many people expect to find every answer in the NEC but it is not the "bible" for everything electrical.
For example:
If this energy chain is part of the machinery, it is not subject to the NEC. The NEC is only applicable to premises (Art 90.2(A)) and therefore only the supply conductors feeding the industrial machinery (Art 670.1).
But, if this energy chain is part of the wiring system that supplies the crane then it is subject to the NEC, including Article 610.
