The Order of the Flaming Rose is a knightly order devoted to the faith of the Eternal Fire. On paper its knights protect the common folk from monsters and unbelievers. In practice they are just as interested in power, and their idea of protecting humans often involves hunting non-humans. The order grew out of the older Order of the White Rose of Temeria, and took on the Flaming Rose as its symbol along with its new faith.
The Order in The Witcher 1
The first game is in many ways the Order’s story. In and around Vizima, the knights fight the Scoia’tael in an increasingly bloody war that tears the city apart. Its Grand Master, Jacques de Aldersberg, is charismatic, convincing and one of the main villains of the game. Some of its knights, like Siegfried of Denesle, are honest men who genuinely believe in the cause, and Geralt can choose to stand with the Order, with the elves or with neither. Whatever he picks, Vizima pays a heavy price, and Geralt ends up killing the Grand Master.
The Order in The Witcher 3
By the time of The Witcher 3, the Order is gone. King Radovid used the knights for his war against Nilfgaard, took their resources and then disbanded them. Many former members turned to crime and now roam the countryside around Oxenfurt as the Fallen Knights, raiding travellers and holding people for ransom. Running into them is a good reminder that shining armour does not always mean a shining soul.