As far as I know dex damage in combat doesn't alter the initiative order because modifiers only matter when the check is made. Since improved initiative is a combat feat, is there anything stopping me to take improved initiative as a flexible bonus feat and after the check is made use a swift action (assuming I made it to level 6) to exchange it for another combat feat?
Since the check has already been made no later modifications to the roll matter. Or to put it another way, if a fighter misses a target a bonus to hit applied later does not make the previous attempt a hit.
The only way it could work is if you were sure you were going to be in a fight and you activated it BEFORE initiative was called for. This seems like it would have a lot of table variation, especially since Martial Flexibility only lasts 1 minute.
Later you MAY be able to use it as an immediate action once it is called for but before you roll. I have no idea how immediate actions work outside of combat rounds.