I think you might have confused a couple details, so a brief history on Karrnath: During the Last War, under Kaius I, the worship of the Blood of Vol was the state religion. Kaius I himself became a vampire and the Order of the Emerald Claw, originally founded as a knightly order to defend the crown of Karrnath, became an arm of the Blood of Vol. With the Blood of Vol to guide them, the Karrns took to embracing the practice of necromancy and began raising the fallen from battles as undead to continue to the fight. This had several advantages, key of which was the fact that undead soldiers required no food, and Karrnath had experienced many famines throughout the Last War. Over the years they honed their craft, producing superior types of zombies and skeletons which possessed their own intelligence and were actually capable of independent thought and leading their own undead forces. While Karrnath still used traditional men and women brought up through the military ranks to lead their armies, they diversified their forces with undead, a practice which most of the other nations found particularly abhorrent.
By contrast. The Church of the Silver Flame originated in the city of Flamekeep (which has the religion as its namesake) in Thrane when a paladin of Dol Arrah allied with a coautl while battling a fiend. The two merged body and soul to defeat the fiend and became an inexorable flame of silver light which persists to this day and is the centerpiece of the Silver Flame religion. Its adherents seceded from Galifar during the Last War and eventually deposed their monarch, replacing the monarchy with a theocracy led by the Church. Thrane and Karrnath were bitter enemies throughout most of the Last War and their religious differences were a key element of their inability to reconcile. The Church of the Silver Flame does not condone or allow the raising or control of undead in any way, shape, form, or fashion (at least not officially; with the grey alignment rules in Eberron there is the occasional evil priest of the Silver Flame who might see things differently). Animating the dead is still an evil act, and the Church of the Silver Flame is a Lawful Good religion.
Karrnath never surrendered during the Last War because no one really surrendered, but everyone lost. After a hundred years the Five Nations (minus Cyre, which had been destroyed) looked upon what destruction they had wrought and decided enough was enough. The Karrns still keep undead legions though because they still have a fundamental agricultural supply problem, among other things. However, the Blood of Vol is no longer the official state religion. It is still tolerated by the people however and remains an influential voice within Karrnath. Its priests are the chief suppliers of undead forces to the military. And the head of the main temple to Vol in Karrnath is undead himself. This is not to say everyone in or from Karrnath endorses the idea of using undead in the military or even the toleration of the Blood of Vol though. In fact, it is one of several reasons for the large Karrn population in Sharn.
Okay, so that was not as brief as I had originally intended. Can you tell I know a lot about Eberron?