It's a very interesting phrase meant to symbolize the dire unrest in several sovereign nations. "Bucky", as he is known in the song, is actually an aspiring photographer, bent on world domination. He "done gun"'ed someone by pointing his gat in their faces and pulling the trigger. That sent the person - let's call him Joey - to eternal hell with the Devil - let's call him Drew.
"We want Bucky Done Gun. We will not fight and run. We want Bucky Done Gun. Get crackin', get get crackin'."