The origins of Cross Burning don't actually lie with the Ku Klux Klan but the Scottish Hill Clans and Thomas Dixon Jr's 1905 Book The Clansman: An Historical Romance of the Ku Klux Klan which predated (and influenced) the Second KKK. Dixon writes

"In olden times when the chieftain of our people summoned our clan on an errand of life and death, the Fiery Cross extinguished in sacrificial blood was sent by swift courier from village to village"

Though unused by the First KKK (Reconstruction Era 1865-1870s) the symbol of the Fiery Cross was picked up by William J. Simmons in 1915 when he started his Invisible Empire of the Ku Klux Klan, the organization's second itineration, with the burning of a cross on the top of Stone Mountain, Georgia. So in reality, it had little to do with the Organization's Christian roots, and moreso to do with contemporary popular fiction and perceived Britannic cultural ties.

Books you should look into

Behind the Mask of Chivalry by Nancy MacLean is an excellent look into the organization and structure of Southern Klaverns in the Second Klan period.

The Ku Klux Klan in the City 1915-1930 by Kenneth T. Jackson is another excellent book detailing the growth of the Second Klan in the northern sphere (Where it was numerically more powerful)

I got a question. Why did the KKK, among other things anti-Catholic, model their uniforms after Spanish capirotes?