Of all the characters in Momaday's book, only two voices speak for themselves. Who were they and why were they allowed to do so?

This is an interesting question simply because it is clear that each section has three different "voices": one mythological, one historical, and one personal. However, it can be said that only two of these voices are actually "characters" and speak for themselves: legend and author.

In regards to legend, the first part of every section is an explanation of a very important myth of the Kiowa tribe.  Here, myth is truly given a voice and made a character for the first time. For example, the first section is the Kiowa tribe's creation myth, which involves the small tribe coming up out of the earth through a fallen log. The tribe is small because a pregnant woman gets stuck in the log (due to her belly); therefore, some of the tribe is left in the earth. 

In regards to the author becoming a voice or a character, the third (often italicized) part of each section is about Momaday's personal story. This part often involves his grandmother, Aho, and her life in reference to the original legend. The creation myth, however, is about Momaday.  Because we find out that "Kiowa" actually means "coming out," we learn through Momaday's voice that the first time he "came out" onto the great plains was a magical moment for him.

In conclusion, it is important to note that it is the Kiowa language that truly connects all the parts and all the sections of this book. In other words, it is language that is of primary importance. Ironically, it is language that allows Momaday to share the two voices you ask about with the world.