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Adding Flurry of Blows to a Swashbuckler seems like a good idea. So let's do that.
Monk Dip
I haven't found anything that extends FoB to anything other than Monk weapons. So, we will need a Monk weapon that also satisfies the "light or one-handed piercing" criteria for most of the Swashbuckler abilities. That means Cestus, Siangham, Lungchuan Tamo, Wushu Dart, Emei Piercer, Fighting Fan.
Cestus and Emei Piercer both modify your unarmed strike. Monks are proficient with the Cestus and it has a 19-20 threat range, so there's really no contest. The Fighting Fan is cooler, of course, but it's a poor weapon, and it's exotic to boot. I thought there was a trait to gain proficiency with a Monk weapon, but it seems I misremembered. Maybe it was a Boon.
As 1. level Monk, we get IUS, FoB (that's what we're here for), a bonus feat (Combat Reflexes?), Fast Movement, an AC bonus, and Stunning Fist.
For Monk archetypes, there's Flowing Monk (feat options, Redirect replaces Stunning Fist), Martial Artist (solves alignment issues), or Sohei (replaces Stunning Fist with the ability to act in a surprise round - winner!)
But I want a Rapier!
Ok, FINE. That's going to require two dips at least. A level of Monk to get Flurry of Blows; and a level of something with Channel Energy, to qualify for Crusader's Flurry. Also, your choice of Deity is Quindiovatos, Besmara, Zura or Cayden.
As for Channel Energy, the obvious answer is Cleric. Crusader archetype will get you a bonus feat, and there's a lot of fun to be had with a Cleric dip.
Life Oracle is another option. So is anything else that grants Channel Energy at level 1 - such as a Necromancy Wizard, or anyone with the Aquatic Domain (or other limited channeling domains). A Spellbreaker Inquisitor shores up the Swashbuckler's Will save nicely. But if you think your GM is going to be difficult about it, just choose Cleric.