Kaito Kosori is the first Unique conflict character that I'm aware of.

Given that discarding extra copies of a Unique character from provinces is a Dynasty-specific ability, I'm guessing one could not discard copies of her from hand to add fate to the copy in play?

Togashi Kazue and Bayushi Kachiko are both unique conflict characters. Discarding unique conflict characters can be done during the dynasty phase only.

Discarding copies of a unique character to add fate on it can only be done during the dynasty phase , but it is not limited to dynasty characters . The rule specifies "from his or her hand or provinces", so conflict characters are definitely included.

Quote

As a player action during the dynasty phase, a player may discard a copy (by title) of a unique character from his or her hand or provinces to place 1 fate on an in-play copy of that unique character he or she controls.