Are the Q from Star Trek a class 6, or 7 civilization?

Types VI and VII are fan fiction.
That said, the Q are categorized as Super Beings (on one account, as a small child, and a very naughty one), and would probably qualify as a VII, if it existed.
Of course, if a VII didn’t want that category to exist, it wouldn’t.

The Kardashev scale is about using more and more energy, and it has always seemed to me that the mindset that would rate technological achievement based on how much energy it uses up, is a very unwise mindset, since, for example:

* energy efficiency is one type of technological advancement
* hopefully an advanced civilization would not want to consume extreme amounts of energy