Did you take `Islands of freedom` quest before finishing `Tackle` quest for Kitano himself ? If you talked with Kitano after getting King`s quest, he no longer need to be persuaded to take you to islands, just tell him `I need to get to islands of freedom, set sail captain` (or something like that). Maybe his dialog are mixed, if you took this quest before finishing his own quest, to defeat pirate who stole his fishing tackle. Just talk to him, and pick all dialog options and wait after dialog closes, maybe ship sailing animation got confused if you closed dialog first time. Save game, talk to him try some dialog choices. If you dont go to islands, load fight some battle and try again with different dialog choices order.
Good luck
