Is Natty Bumppo a flat or round character?
If we can define "round" characters as complex or ones who are multidimensional, then I think that Natty Bumppo could be seen as round. He is not singular or monolithic in Cooper's descriptions of his experiences:
Hawkeye [Natty Bumppo] is in his thirties, at the peak of his physical powers. Civilized, mannered, and garrulous, he can at times be humorous and long-winded, or give over to boasts and superstition. He is a man of dual natures, however, and can be as stoic and silent as his Indian companion, Chingachgook. Although a somewhat idealized character, Hawkeye is not without his flaws. He is always quick to point out his "blood without a cross," making sure that none mistake him for an Indian or even someone of mixed heritage. He is also prejudiced—quick to pass judgment on the Indians of the tribes other than the one with which he is allied.
Of particular mention would be the idea of Natty being of "dual natures." This makes him a round character because of the complexity present, allowing him to be seen in multiple lights and not completely in one mindset. As Natty grows in the narrative, he reveals this complexity in turning his back on White culture and embracing the idea of being "the last of the Mohicans:"
....the character of Hawkeye (or Nathaniel Bumpo, also Natty) grows in small yet subtle ways, developing as a human being who has shunned the “civilized” world of the white man in favor of the natural environment of the Native Americans by whom he was raised. Yet Hawkeye retains some characteristics that he learned exclusively in his youth and have transferred with ease into his new life.
This conception makes him a complex and round character.