My Third Great Grandfather, David Fleming

According to family lore, David Fleming, my third great grandfather, died in the War of 1812. The War ended in 1815 principally with Americans routing the British with the help of Jean Lafitte at the Battle of New Orleans. David Fleming was supposed to have died within a few days of this battle in Mississippi.
I had attempted to find his burial location in the south with no results. I decided to give the question to the National Park Curator at the Jean Lafitte National Park where the battle was fought. There is a military cemetery there but it was really established for Civil War burials and only four veterans of the War of 1812 are buried there.
I kept looking and was able to locate his burial here.

David's last name was misspelled as Flemming, which was not surprising. What did surprise me was that he is buried in the War of 1812 Cemetery in Erie County, New York. I found that he was part of the 17th Kentucky Infantry and that he died from fluid in the lungs. Many soldiers died of disease in this war.
He was born in Pennsylvania, fought for Kentucky, died in Mississippi and is buried in New York. And his children filed for benefits in 1828 at a court house in Trumbull County, Ohio. In their affidavit, they mention the 17th Regimental Infantry. The 17th may have been a U. S. Army unit which organized in Kentucky.
David was married to Eleanor King, the daughter of Colonel Robert King, who was an officer for George Washington at Valley Forge.
I have begun the process to apply for membership in the Sons of the American Revolution through Colonel Robert King. It is somewhat daunting in that you have to prove your direct lineage and I am concerned about what will constitute acceptable proof. But there is a new chapter in my area and they will help.