http://www.city-data.com/township/Big-Creek-Sebastian-AR.htm...
This mentions Red Oak Cemetery.

I like to use/contribute to findagrave.com.
Doesn't look like Red Oak has any Fletchers or many graves that old.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gsr&GScid=...

I do see from the 1840 census that he was in that area which was upper Crawford county then, but is now Sebastian county (incorporated in the 1850s) and is now the Lavaca area.
http://www.myheritage.com/research/collection-10124/1840-uni...

Doing a little digging, I found a few trees with a Charles Fletcher with those dates.
http://www.myheritage.com/research/collection-1/myheritage-f...
http://www.myheritage.com/research/collection-1/myheritage-f...

Sorry I can't help more.