I think the jury's out on this one, with conflicting evidence both for and against.
Whenever the question is asked here, flat earth members say it's not true.
A
recent yougov poll of over 8000 Americans, however, returned figures saying that 52% of flat earthers considered themselves "very religious", while another 31% considered themselves "somewhat religious".
Most flat earthers live in the States, where about 75% of the population identify as Christian - so it stands to reason that there'd be a fairly high crossover there.
And some of the most prominent flatearthers, such as Samuel Rowbotham and Rob Skiba are most definitely Christians, while many people I've talked to believe the reason The Powers That Be teach the globe is "to hide God."
Anyway, if we assume most flat earthers are Christian, one of the the reasons "why?" would be because they find the notion of a spherical earth orbiting a sun in contradiction to The Bible, and to their belief that we humans are at the centre of God's creation.
Note: only a small percentage of Christians believe The Bible to be "literally true" - these are known as "Biblical Literalists" - and so, for them, they are required to shoot down anything that challenges that belief, and to perform the most dextrous mental gymnastics to explain away the inconsistencies and errors (see: cognitive dissonance).
For most Christians, it isn't important that The Bible is viewed as "literally and word-for-word true", and they understand that many of the notions contained within it are merely reflective of the understanding of the people at the time - including views on science, cosmology, the universe, etc.
To summarise:
Are most flat earthers Christian? We're not sure.
Are quite a lot of flat earthers Christian? Looks like it.
Why would the belief in the flat earth particularly appeal to Christians? Partly because it helps them feel more secure in the world and in their faith in The Bible; and partly because it helps them feel less insecure if they believe we're being watched over and are especially loved by God, in an enclosed space, rather than floating through the unimaginable vastness of the mostly empty - as far as we know - universe. Plus other reasons besides.