I never found Balthier to be 'flirty' in a romantic sense - I mean, it's not like tries to ingratiate himself with the women in order to win their affections; he certainly never tries to seduce anyone. He definitely lays on the charm, though, which seems to stem in part from his natural charisma and sophistication, and in part from the bluff showmanship he uses to create the 'dashing sky pirate' image he presented to the world to hide his past and his various agonies. He's definitely aware of his limitations, rather than thinking excessively highly of himself; I reckon it's obvious to him that his act doesn't really fool anyone who's come to know him.

Ashe, for her part, probably just cares about Balthier as a friend and companion, someone who helped her out - despite his own better judgment, apparently - when no-one else would or could. His apparent (SPOILER)sacrifice is what saved Rabanastre, after all; everyone who knew Fran and Balthier was affected by what they did.

Still, my earlier point remains: Balthier/Fran otp, imho.