Louie Gohmert was co-chair of the Congressional Prayer Breakfast this year (along with Janice Hahn D-CA) and so it is possible that the prayer breakfast committee promoted this to the African leaders. It is also possible that Barton sponsored it and used his relationship with Gohmert to spread the word.
Hard to say which stories he told. Perhaps he told them Congress printed the first English Bible to use in schools, or that most of the founders had seminary degrees. Despite the fact that even the Family Research Council removed a video of this presentation, Barton is still giving it, this time to international leaders.
The Fellowship Foundation helps to plan and run the prayer breakfast. When I attended in 2010, I attended the African breakfast and other events and did not hear Christian nationalist messages. All in all, it seemed pretty tame from a political perspective. I cannot imagine how this presentation by Barton would support the mission often articulated by the Fellowship.