Like in this picture of his meeting with Livingstone:
http://libweb5.princeton.edu/visual_materials/maps/websites/africa/stanley/stanley1-4.jpg
Henry M. Stanley was a very strange character (If you've ever read King Leopold's ghost you know this). During this picture he probably brought the American flag because America was the place he lived the longest. He even took the name Henry Stanley from a shipping master whom he worked under in New Orleans. His voyage to find Livingstone was actually sponsored by New York Herald Publisher James Gordon Bennett which is probably why he used the American flag instead of another countries. However, his later voyages were sponsored and funded by King Leopold II of Belgium, and he worked under the flag of the International African Association (a yellow star with a blue background to symbolize the bringing of light to the dark continent).