The Farlaf Order is an organization that was mentioned by C.C. that was created after breaking away from the Geass Order and by the way some members still refers to V.V. with some reverences and seems to know C.C. it can be hinted that the breakup of the two group only happened not so long ago.
Description[]
The Farlaf Order despite being formed after a falling out with the Geass Order seems to have long history with the region of Zilkhstan dating back almost 300 years ago to the founding of the country. As shown through their symbol being adopted as a national flag of the country. Hinting that the reason the country exist in the first place was because of their group intervening in favor for the creation of the country. Or they could be a new group merely adopting the tradition of the old group that used to called Zilkhstan their home.
As stated earlier there are possibility that the Farlaf was instrumental in the creation of the country and that means the creation, the continuation and prosperity of the country was maintained through the use of Geass throughout the centuries. The same way Shamna used her power of "prophecy" to guide the direction of her country. This explains why the country has never been defeated before despite being much smaller. There's also possibility that every Zilkhstan Royal family were given Geass the same as Shamna by members of the Order in order to protect the country and the Order from outside threat.
Not much is known of what the Farlaf Order did when it's still a part of the Geass Order other than admitting Shamna and Swaile into the organization. The only thing that is known is that Farlaf was researching a way of connecting to C's world through an intermediary through the use of a blood relation.

Farlaf priests conducting a ritual.
During the second year of the Kowa period the Farlaf Order currently resides in the Temple of Zilkhstan and remain as an influential organization inside the country even becoming the face of the religion of the Kingdom of Zilkhstan and it's moral authority. It is unclear whether or not that each members of the religion are all members of the Farlaf Order and knows about the existence of Geass or is that not all members of the religion knows about it and only a select few knows about the going on inside the temple. While the rest are true believers.
It is also hinted that the Farlaf Order operated a group of assassins under the command of Swaile to hunt down enemy of the State like the Black Knights and other such entities that poses a threat.
The Destruction of the Temple[]
It is unclear what happens to the Farlaf Order after Lelouch destroyed the temple and buried the High Priestess inside. Whether or not they are still allowed to exist under the UFN occupation or not is remain to be seen.
Relationship with the Geass Order[]
As shown, despite having broken away from the original order centuries ago, its been implied that Farlaf still maintained some relationship to its original organization. This is shown where its members are seemingly up to date with the Order’s leadership and status referring to the directors of the Order who bear the Code of Immortality as “Masters”.
With them having been familiar with Order’s former leader V.V. and and its predecessor it is understood that they were aware of what exactly had happened with the Sword of Akasha and how Lelouch was responsible for altering C’s World and the Geass Order’s relationship with Charles zi Britannia.