A few things I noticed:
1) The "Charisma score + 4" seems a bit much for the number of Flair uses per day. I would cut it down to maybe 4 + Charisma modifier at the 1st level of Dashing Swordsman, plus 2 more uses per level of Dashing Swordsman. So, at full Dashing Swordsman, that's 22 uses, plus the character's Charisma modifier, which is a good number, without giving too many Flair uses to people who only dip into the class who happen to have very high Charisma scores.
2) The Dramatic Entrance ability seems much too mechanics-heavy for something you'll possibly be doing every battle, especially having to get the CR of the encounter from the DM. I would change it to something much simpler, like after all Initiative is rolled, you can expend a Flair usage as a free action and roll a d20 + 1/2 your Dashing Swordsman level + your Charisma mod. If your result equals or exceeds the highest Initiative rolled for the current encounter, you may place yourself anywhere in the Initiative order you choose (letting you choose the time where it would be most dramatic for you to act), and may get a Surprise round, if you so choose (which isn't that powerful, considering you can only do a single action (move or standard) in the surprise round RAW).
3) I would change Thespian's Luck to simply being a Flair usage ability, with my included statement on changing the number of uses of the Flair ability per day, rather than a number of rounds equal to your Charisma modifier. It would make usage of the ability more tactical, since the Flair ability can be used for so many other useful class features.
4) Better Lucky than Skilled seems a bit too detrimental and restrictive for something that has the potential to be completely useless (since with two dice, you could still roll low on both). Instead, I would change it so that by expending a Flair use for the day, you can reroll any dice roll, but you must choose to use the ability before the results of the original roll are revealed, and must take the rerolled result, no matter what it is. Also, remove the exhausted/unable to use other class features penalty, as it seems unnecessary for an ability that doesn't have a guaranteed benefit (as you could still roll low again).
5) Also, simply from a presentation perspective, I would move the level 1 Dashing Swordsman ability to add his class level to a skill check by expending a Flair use to it's own separate ability, and put Flair and it's number of uses per day on it's own, so as to present Flair as more of it's own class feature (since it's used so much for so many other class abilities) and not tied to the skill enhancement class ability.