Did Christians really think the earth was flat? The answer is no.
Jeffrey Burton Russell, Professor Emeritus of History at UCSB, thoroughly discredits this idea in his book Inventing the Flat Earth (1991). He explains that the idea was started and spread in the 1800s by individuals such as Washington Irving, Antoine-Jean Letronne, John William Draper and Andrew Dickson White. Contrary to their ideas, Russell points out that those living in the medieval era knew the earth was a sphere. And this fact was known by the vast majority of educated people as far back as the ancient Greeks - hundreds of years before the medieval era.
In addition to Russell, other historians have been making this same point for decades. Given this, one might wonder why the idea continues in the modern mind. Russell gives his opinion on the matter in the following quote.
The reason for promoting both the specific lie about the sphericity of the earth and the general lie that religion and science are in natural and eternal conflict in Western society, is to defend Darwinism. The answer is really only slightly more complicated than that bald statement. The flat-earth lie was ammunition against the creationists. The argument was simple and powerful, if not elegant: “Look how stupid these Christians are. They are always getting in the way of science and progress. These people who deny evolution today are exactly the same sort of people as those idiots who for at least a thousand years denied that the earth was round. How stupid can you get?”
But that is not the truth.
Jeffrey Burton Russell, “Myth of the Flat Earth,” American Scientific Affiliation Conference, August 4, 1997, http://www.veritas-ucsb.org/library/russell/FlatEarth.html.