DeJonge says the project has cost about $200,000 already.
Arkansas showings are set for May 13 and 14 in Malvern, May 15 in Little Rock, May 23 in Marshall and May 25 in Hot Springs.
Missouri screenings are set for May 20 in Buckles' birthplace, Bethany, and May 21 in Lamar.
Hundreds of schoolchildren are expected to attend the Bethany screening, where the film will show repeatedly from 9 a.m. to 9 p.m. The owner of Big Time Cinema didn't immediately return a telephone message about the event.
Buckles lied about his age to enlist at 16, then went on to outlive 4.7 million other Americans who served.
He never saw combat, serving instead as an ambulance driver in England and France. After Armistice Day, he helped return prisoners of war back to Germany.
He returned to the United States in 1920 as a corporal. During World War II, Buckles was working as a civilian for a shipping company in the Philippines when he was captured as a prisoner of war. He spent more than three years in Japanese prison camps.
Buckles was buried at Arlington National Cemetery after hundreds of people paid their respects. His grave is on a hillside within view of the Washington Monument, Capitol dome and Jefferson Memorial.
At the crest of the hill sits the grave of Gen. John Pershing, under whose command Buckles served.