Smoke Signals is basically about a guy named Victor and his relationship with his father or lack there of. It also brings in a lot about Native American reservations and traditions, especially the oral tradition. The custom of story telling is important in Native American tradition and there for prominent in the film. It is used as narration, as a trigger for flash back sequences, and as insight into Thomas and Victors characters.
The movie starts off with Thomas's narration, and it's scattered through out the film. So you get a sense that it is all one of Thomas's stories. The method strengthens the importance of Thomas's character. The plot would focus more on Victor if Thomas wasn't narrating in bits. That technique also emphasizes the importance of the oral tradition in Native American culture.
Story telling is a part of the Native American tradition that Thomas has really taken to heart. He takes just about every opportunity possible to tell a story. It is used in the film to trigger flashbacks. These flash backs are extremely important in the development of the characters and conversely important to the plot.
The stories are frequently about or concerning Victors father. The stories hit a nerve for Victor, and I don't think Thomas notices it. Victor is angry and resentful of his father, for being a terrible parent and for leaving him and his mother. He is also jealous of Thomas because Thomas has better memories of his father than he dose. He thinks that his father treated Thomas better, the way he should have done his own son. All of these sort of under running problems are spelled out in the flashbacks.
These are the ways that the Native American oral tradition plays an important role in the film. It is important in narration, flashbacks, and most importantly in character development. Without the stories and/or flashbacks to define the characters and their history the plot would be much less