Hi Mike, welcome to the game and boards.

I can see where you aren't quite right, and I hope I can explain it.  I'm going to refer to the sequence on page 172.

Flair is applied in step 2, as an incentive not to rely on the same skill for every roll.  It is more likely to turn up in action scenes because they have multiple rounds of rolling dice.  This acts as an incentive to have multiple skills at a level where they can be invoked.

Improvising happens during step 6 if a player decides they need to do something outside of their initial approach.  It is more likely to turn up in dramatic scenes because you are covering a lot of ground with one roll of the dice.  That said, there's no reason why you can't improvise in an action scene, probably as a result of suddenly revealed circumstances mid-fight.  This acts as a disincentive to the everything looks like a nail effect.  "You're going to a Grand ball."  "I roll Finesse+Weaponry because it gives me 9 dice and my Convince is only 6."  "But, you'll need to spend 2 raises to do anything other than stab people!" "Okay, I'll roll the convince then."

An example could be that one of the party goes down during a fight and someone else wants to get them out of danger immediately, because that Villain still has Danger Points and Raises left.  However, their approach was to use Aim for shooting at the enemy, which really doesn't cover either dragging them or interposing yourself.

As you can see, both rules are actually incentives to make rounded characters. 

I hope that helped.

Joachim sums the distinction up nicely, but in short:

• Flair provides a bonus for the roll/Round for players changing things up and making the game more interesting through their descriptions. It would probably be seen most in Action Sequences, where you roll every Round. This gives a slight advantage to the player who goes from "I wade into the boarders with my sword," to, "I draw pistols and fire on the enemy Captain," to, "I chase him into the Ship's rigging," in subsequent rounds over the player who just states that they, "duel with my sword," each round.
• Improvising / Changing Your Approach gives a slight penalty while spending Raises for changing a plan in mid-action, or going against your current momentum. You're trying to snatch a document mid-duel, or stopping a charge to protect a friend, or take the opportunity to knock out a guard at the ball you're trying to keep up a facade as a common coutier at. Mechanically, it also penalizes a player from just leaning on their best ability all the time - otherwise, you'd potentially have players trying to convince the GM to let them use whatever their highest skill is in every single situation, and never actually apply that skill within a Sequence.

Flair encourages changing things up to make the game interesting, but both rules work against abuse of a character's "best" abilities within the game.

What is sticking for you is the lack of dice rolling that you normally see in a game. Maybe I start a sword fight by drawing and waiting into combat (finesse and Weaponry). I get flair because it it's the first fight. Next round I decide to keep fighting by leaping around the villain and off the walls to confuse where the attack will come from ( now it's finesse and athletics). I still get flair. But my ally is in trouble this round and I really need to shoot his opponent across the room . Shooting has nothing to do with leaping so it costs me an extra action to do it. (The improvise penalty). The next round we decide to flee and running away is athletics and finesse ( no flair). If I need to hit the villain during this round, that is fighting and not running so I imcur the improvise penalty for that. But if i grab a rope and swing away, that would fit athlete so no penalty.

Ok, let's adjust terminology. Dramatic Sequence and Action Rounds are both the same thing. We will call them "sequences" for this. When a Sequence starts you declare intent and roll dice. That gives you raises to use in the sequence. (This is when flair is applied). Each time you want to do something in the sequence, that is an "ACTION". Each action costs you a raise. If the action is not in line with imtent (improvise) you pay an extra raise. There is no dice rolling for ACTIONS, just pay the raise. As for earning Flair... That is dependent on first use in the game SESSION. So if you play for four hours and have 6 Sequences, Flair for Resolve+Perform only happens the first time you use it. If you have 4 fights, Weaponry+Finesse only gives flair bonus in the first round you use it in of the first fight of the session you use it. (Creative description always works to add flair at GM discretion and might get you combos using that skill with the other 4 Traits for flair).

Tips for getting flair: you have 5 traits to combine a skill with. Find a way to do what you want with each in a combat. Round 1 you can declare a basic dueling plan and get Weaponry+ Finesse. In round two, maybe describe looking for weakness to exploit and use Weaponry+Wits. In round 3 you can try to humiliate him with tagging and elegant footwork for Weaponry+Panache. Get to round 4 and you can try to force him to his knees with a corps a corps for Weaponry+Brawn. Should it reach round 5, you can just try and wear him down with your superior training and a rapid fury of blows to tire him out and use Weaponry+Resolve. If it goes past that, switch to Aim and shoot him.

The key is that the goal is not rolling dice for everything a player does. An action sequence is like an old system combat round but raises are both the initiative result that tells us how many things we can do AND replace the combat rolls on those actions. Players can end a fight in a single action round and it can be quick. Other times it may involve chasing a fleeing opponent and stretch time a bit. Each raise might be an attack. Another player might use theirs to rob the place during the confusion of a fight. A dramatic sequence might be all climbing, leaping and swinging chases through a city.

Flair requires Stylin' & Profilin' and trips to Space Mountain and WHOO~!!!!!

Here is another good example for flair skipping around on skills instead of traits.

Fight breaks out in a building.

round one I opt to draw a blade and duel the opponent (weaponry+finesse)

round two I opt to run up the walls to avoid his attacks while getting around him to attack from behind. (Athletics+Finesse or maybe Panache)

round three I opt to lure him outside where my friends are and improvise a few blows on the way (Intimidate or Tempt depending on description+wits)

round four turns out my friends left so I draw my pistol and shoot him (aim+finesse)

round five I decide to get out of town while he grabs his knee in pain (hide+resolve)