If we compare it to flat dmg per attack and take into consideration usually low AC numbers on BGTSCC content it's not even 1 dmg per attack. Let's take usual fighter with 6 attacks, and assume 4 of them hit which is quite realistic for majority of the content. Since most of the time we're unable to make the feat work every 2 rounds (it's almost always 3 rounds, sometimes 10 if you forget to click it for a while but lets say 3) its 3 x 4 attacks that hit which is 12 attacks. Average of 2d6 is 7 so there we have it. 7/12 and turns it's equivalent of 0.58 dmg per attack. Even super weak feat of weapon specialization gives 2 points of dmg and Flourish is equivalent of 0.58 dmg
TLDR: Taking all that into consideration I'd say 1 round (6 sec) of cooldown would be semi decent and made the feat at least comparable to weapon spec.
If the buff seems too much then at least add some QoL and turn it into a mode so Flourish happens automatically and reliably every 2 rounds in similar manner that Expose Weakness now works.
Flourish
At 6th-level, Duelists can make an impressive, flashy attack with a piercing weapon that catches their foe off guard. This attack deals 2d6 additional points of piercing damage. There is no limit to the number of times per day the duelist may use this ability, but has a 12-second “cool down” between uses. This Feat WILL work with weapons that have Piercing & Slashing damage Type, such as a scythe or halberd.
