I'm not going to be able to offer you a lot of feedback on balance and such, because I'm not familiar with OA at all. I can offer a few things, however.

Quote Originally Posted by Melifaxis
Pre-Requisites:
Alignment – LG or LN
Base Attack Bonus +5
Proficiency with daisho
Accepted into the Brotherhood by a current member
Spoken with a Ki-Rin
Empty Hand Mastery
Tumble: 4
Knowledge (Religion): 4
Knowledge (Shadowlands): 4
Handle Animal: 5
Ride: 5
This doesn't match the "general" format of pre-reqs, and could probably be made easier to read if you altered it slightly:

Alignment: Lawful Good or Lawful Neutral
Feats: Empty Hand Mastery (I'm assuming it's a feat), Exotic Weapon Proficiency (Daisho) (I'm assuming it's a weapon and it's exotic)
Skills: Tumble 4 ranks, Knowledge (Religion) 4 ranks, Knowledge (Shadowlands) 4 ranks, Handle Animal 5 ranks, Ride 5 ranks
Special: Spoken with a Ki-Rin, and also Accepted into the Brotherhood by a current member

Formatting aside, the requirements seem really steep for a monk. Unless there's OA rules that change this, Knowledge (Shadowlands), Handle Animal and Ride are all cross class skills. That's is a lot of skill ranks to require cross-class.

Quote Originally Posted by Melifaxis
Class Skills:
Balance, Bluff, Climb, Concentration, Craft, Diplomacy, Escape Artist, Heal, Hide, Jump, Knowledge (religion), Knowledge (arcane), Knowledge (Shadowlands), Listen, Move Silently, Perform, Profession, Ride, Spot, Swim, and Tumble.
You forgot to mention how many skill points per level. ;) Also, do you have Knowledge (Arcana) and Perform on your list for any particular reason, other than they're also Monk skills? My general rule of thumb is that a skill list assigned to a Prestige Class should fit the new class, not the most likely base class used to enter the class. If that makes sense. ;)

<<snipped the table>>
You don't mention weapon and armor proficiencies at the beginning of the class features description. ;)

Quote Originally Posted by Melifaxis
Dance of the Daisho: Both the Katana and the Wakizashi can be used as unarmed attacks per the monk rules/restrictions. However, if one wanted to wield both simultaneously, they would still need Exotic Weapon Proficiency: Katana.
Do you mean they can flurry with the weapons? Is that the intent of this?

Quote Originally Posted by Melifaxis
As the Body: A brother or sister of the ki-rin can do their unarmed damage with a daisho. For example, the katana is no longer limited to d10 as base damage; instead a monk used his/her unarmed damage per the table in the Player’s Handbook.
This isn't as good as it sounds, at least as written. You should add a first level ability that allows this class to stake with monk levels for determining unarmed damage. Otherwise, the d10 of the sword will always be better, unless the monk enters this class real late. You may also want to increase other monk abilities, too, such as ki, AC Bonus and/or Fast Movement.

Quote Originally Posted by Melifaxis
Wisdom of the Ki-Rin: Before progressing to this level, a brother or sister of the ki-rin must seek out the living embodiment of their clan, the ki-rin, and offer to assist it in any task it chooses. In exchange, the ki-rin will impart a portion of its wisdom and teachings to the monk granting him/her a permanent +2 bonus to Wisdom.
The timing of this is a little ironic, as there has been a discussion on another board a frequent about whether or not pre-reqs within a class (such as this) are good or bad. I'm generally not a fan of them as a concept, though this one isn't too bad. It has the potential, though, for a DM to screw the player by not arranging for the meeting to take place, and that could be a problem.

You should type the bonus - probably Inherent.

Quote Originally Posted by Melifaxis
Ki Strike +1: As per the Player’s Handbook.
Very weak class ability, especially for this late in the class.

Quote Originally Posted by Melifaxis
Ride the Wind: Once per day for every two levels, the brother/sister may fly as per the spell or confer the gift of flight on another.
Caster level? Duration?

Quote Originally Posted by Melifaxis
Diamond Soul: As per the Player’s Handbook. SR of level +10.
Class level, or character level? If it's class level, it's very weak.

Quote Originally Posted by Melifaxis
Fury of the Ki-Rin: Once plus his/her wisdom modifier times per day, a monk may invoke thunder on their unarmed strikes doing an additional d6 sonic damage per successful unarmed attack. The aura lasts for 1 round for every two levels of the brother/sister of the ki-rin. This ability may only be used against those who carry the Shadowlands taint or who are evil in alignment.
Nice, but weak in my opinion. I think I'd remove the limit on the number of times per day - the ability is already focused enough to make it so it won't be used against everything.

Quote Originally Posted by Melifaxis
Riddle of Invulnerability: At 10th level brothers/sisters gain damage reduction 20/+1.
This class is obviously written for 3.0? ;)

It sounds like a great ability, but this is kind of weak. It's really only going to protect the Monk from the attacks of animals, since just about every humanoid foe at this point will have a magical weapon.

Quote Originally Posted by Melifaxis
Mind of the Ki-Rin: At 10th level brothers/sisters can communicate telepathically, but only with those they could normally converse with. Thus language restrictions, and distance apply
Nice flavor ability.

***

I know I sounded really critical (it's becoming a common theme, it seems). Some of my comments might be trumped by things in OA that make the abilities better, of course. The class has nice flavor, in my opinion, but comes up a little short on the power scale. We're talking about a character who is at least 7th level (and quite likely higher) upon entering this class. That means we're talking about a 17th level character when discussing the 10th level ability. I want more bang for my buck at 17th character level.