Rayleigh's statements:
The most important information about haoshoku haki came from the dark king in chapter 597. The first thing Rayleigh says about Haoshoku,
"it is the power to overwhelm -- the color of the supreme king"
Cnet128's translation is a little more clear:
"This is the ability to overpower the opponent's will"
Rayleigh also said, "
It can often be found in the type of people who make a name for themselves on a global scale" (cnet128's scripts)
So the next criteria can be =>
4) fame on a global scale
Chinjao and King's statements:
Chijao asked Luffy, "
What king do you seek to be?"
This statement implies the CoC users are typically aiming for a title/throne. Thats why the next criteria can be =>
5) ambition to be a king
UPDATE:
In Chapter 1033, King said it again once Zoro unlocked his AdCoC:
Some scanlators were more direct with their translation. They translated, "So you also have kingly ambitions?"