I'd just like the clarify that OP seems to be talking about the movie "Django Unchained" (2012), and not the movie "Django" (1966).

At the risk of being one of the deleted comments; the info I have found suggests it was purely symbolic and did not have a reference in historical fact.

This guy looked into it just as you, here's his response:

http://movies.stackexchange.com/questions/18070/why-did-john-brittle-have-bible-pages-sewed-into-his-shirt

Here's the guy's money quote:

So in summary I think the Bible pages are there to demonstrate his belief that he is one of God's servants. I think they also serve a double purpose as his death and bleeding out on top of the scriptures symbolise "justice" being done given his false beliefs

And here is another fascinating exploration of the various Christian themes and symbolism in Django Unchained, which explores that scene a bit:

http://c3.umhb.edu/blog/christian-themes-django-unchained

And here's THIS guy's money quote:

The first bounty Django collects is for the Brittle Brothers. As John Brittle prepares to whip a slave girl for breaking eggs, he has Bible pages pinned to his coat as he fervently quotes an Old Testament passage about justice. When Django shoots him, he shoots through one of these pages that covers Brittle’s heart. Red blood flows out of the bullet hole, onto the page, almost symbolically purifying the page with the evil zealot’s blood. It’s an image that foreshadows Calvin Candie’s assassination, though his heart was covered by a white carnation.

I am NOT a historian of this era; simply trying to offer a few external sources the OP may not have found. Mods; please feel free to delete if this does not make the cut.