The Fist of Shadow was a part of the Kinkou order before Zed's arrival, so that must be taken into account. It is possible, as I see it, that Zed's powers come from the same place Akali's do; that box. It would tie in nicely with the idea of balance Ionia presents:
Shen is an Ionian who very clearly walks between Light and Dark.
Kennan is the member of the Kinkou that is heavily invested in the Light side.
Akali, therefore, must fill out the latter end of his spectrum: becoming the Dark side and gaining her power from some kind of similar source.
This theory, of course, does not rule out the potential they are related in any way (be it by blood or mentorship) and I would also love to see that kind of potential played out in character development.