A Flayed Man Has No Secrets and Tywin Lannister NCU

If A Flayed Man Has No Secrets is played to cancel Tywin's Rains of Castamere effect, can Tywin's ability be played on another turn, or is it considered as already used?

YES

YES, you can use Tywin's Rains of Castamere on another turn.

Since the Season 4 FAQ all the targets of an ability needs to be pre-declared, even if there are prerequisites to use that ability, so in the target declaration step of Tywin's Rains of Castamere the opponent can use A Flayed Man Has No Secrets to cancel the whole effect, even the "Once per game" part of Tywin's Rains of Castamere.