During Heavensward it was Estinien but overall Kaoru's best friend is Thancred. They had a minor crush on him from when they met him but it faded when they met Haurchefant.
Its really during Shadowbringers that their friendship gets elevated to best friend. Kaoru is having a very difficult time emotionally and keeps trying to hide it from everyone but Thancred can see right through the act and he comforts them when they feel like they have no one else.