No, Abraham Lincoln didn’t write the Gettysburg Address on the back of an envelope.
Judging from the many drafts of the speech that have been discovered, the speech was fashioned through the traditional method of writing and revising.
It was presented on November 19, 1863, at the dedication of the national cemetery at Gettysburg, four months after the Battle of Gettysburg.
The original copy of Lincoln’s Gettysburg Address can be found in the Library of Congress.