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Depending on what you're trying to do it probably wont matter.
Regardless of how many arms you have you still will only be able to make X number of attacks per round and no matter what the Damage for Unarmed Strike will always be the same.
The rule you're referencing there exists to clarify that just because they have more arms does not equate to them having more than 1 "main hand" for the purpose of attacks, damage, and effects.
Normally you only make one attack, plus one for every 5 points of BAB after 1, with your "main hand" each round.
Flurry of Blows and TWF work the same mechanically... each gives you an extra "off-hand" attack each round. Flurry of Blows scales with your BAB to include the Improved TWF attack later on.
Improved Unarmed Strike eliminates the whole "off-hand" being only associated to hands, now you can pelvic thrust or headbutt or whatever.
A 4 armed alien with Flurry of Blows/ TWF still is limited to one attack, plus one for every 5 points of BAB after 1, with its "main hand" each round... and one extra "off-hand" pelvic thrust from Flurry of Blows. Maybe an extra extra "off-hand" attack with a high enough BAB, since Flurry of Blows scales with BAB.
The true genius of the 4 armed alien is its ability to wield two Butchering Axes and do fun TWF/Double Slice/TWRend shenanigans as the 2-Handed Fighter archetype, abusing the Backswing class ability with TWF...
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If your GM allows you to take it, as a four-armed Kasatha, you wouldn't take Two-Weapon Fighting, you would take the Multiweapon Fighting feat.
NOTE that you DO NOT need to take Multiweapon Fighting to use Flurry of Blows. You would only take it if you wanted to use the Two-Weapon Fighting rules as modified by multiweapon fighitng) INSTEAD of the normal Monk rules for making unarmed attacks. Under the normal Monk rules, there is no such thing as an off-hand. If you use Multiweapon Fighting, then you have a primary attack and secondary attacks, similar to two-weapon fighting.
If you take a monk archetype that removes Flurry of Blows, then using Multiweapon Fighting is a reasonable substitute.
And if your GM allows it, the Unchained Monk is much more satisfying to run than a regular old-fashioned Monk.
Goodluck and have fun!
Outside of Flurry... assuming a Improved Unarmed Strike and Monk... for a single attack, everything on your body is your "main hand" for your single attack.
You can punch with any of your four hands, or pelvic thrust, or headbutt, or shoulder strike, or knee strike as your "main hand" in a single attack.
This is the same for any Monk with Improved Unarmed Strike, regardless of how many limbs/heads/appendages he or she may possess.
In a full attack routine, that is not Flurry of Blows or TWF based, you can attack with any part of the Monk as many times as your BAB allows you to attack in the round.
The race in question has specific restrictions about the use of its extra arms providing extra attacks.
Every other known avenue to get extra arms comes with the exact same or very similar restrictions.
I see your logic, but literally everything in this game denies this exact loophole from being available without dedicated effort.
If you want to be a Kasatha Monk with ALL THE ATTACKS... you need to make ALL your hands claw attacks and take Feral Combat Training with Weapon Focus Claw, or ditch Flurry for MultiWeapon Fighting.
Having four arms as a playable race does not give you the natural attacks of your enemies with four arms, and it shouldn't... otherwise the game has no way to make itself challenging for the players.
Find a way around it... because in the expansive universe we all know and love called PF1, there are workarounds.
You are asking for everything at the price of nothing, come on.
But to get this all in order... you want to have a Flurry of Blows routine, FROM LEVEL ONE, that involves 4+1 attacks at your Monk's Unarmed Strike Damage? And you want this routine to scale with your BAB, and have additional KI Pool added strikes to it? So you can abuse something like Jabbing Style with 5+hits per round?
Honestly, I would completely let you do it because this game takes great pleasure p!ss!ng on martial characters... what? You are twice as scary as a completely nerfed martial combatant? Lol!!!
This is exactly why you can completely TWF Butchering Axes as a Kasatha Two-handed Fighter and nobody cares!
If your GM is allowing the race to play, yet still nerfs the extra martial capability of the extra arms, I don't really have an answer for you. It's so much easier to say that there are no 4 armed alien characters allowed, than to further nerf low-Tier martial characters... in my opinion. Extra arms, extra weapons, extra attacks... YES, PLEASE!
Martial characters getting p!ssed on is tiring. Just let them play. No matter what they ever do, it's absolutely nothing compared to a single class CRB Wizard... who f!ck!ng cares?
You can attack twice as many times and I can stop time, create my own plane of existence, and summon horrendously unimaginable beasts to fight in my place... goodbye!
PS. Can you freely travel between the Planes?
... because I am sending you to the Plane of Water.
... by the way, can you breathe water?
[Says the Wizard as he kills every martial character, ever]
Re: Martial/caster disparity:
The game kind of assumes that your party can achieve certain things out of combat at certain levels (no invisibility before level 3, no flight before level 5, no teleportation before level 9), can achieve certain things in combat at certain levels (can't detect the invisible before level 3, no freedom of movement before level 7), and can do a certain amount of damage at each level. That's kind of the entire basis of the CR system, actually. And that damage that the party can do is typically the realm of the martial classes. You can argue that having one class that can do anything effectively but HP damage and another class that can't do anything effectively but HP damage isn't good game design, but you really can't argue that the ability to do more damage than is expected for your party's level doesn't skew the balance of the game.