Does it work with air slash and other flinching moves when they fail? I mean this:
after 'air slash' fails to cause flinch 'king's rock' effect activates and gives 10% chance o cause flinch anyway (20% with serene grace)
I got conflicting into on that from diffrent sources. It seems to work at least to some degree because bosses use Togekiss holding this item.
 

It's as the Bulba description for Gen 5 onwards says.

"Grants all attacking moves that do not already have a chance to flinch a 10% chance of causing each target to flinch."

So if a move does not have a chance to flinch it gives the move a 10% flinch chance.
This does not apply to moves like Air Slash that already have a chance to flinch.

thank you