How can Such a Long Journey from Rohinton Mistry be read as postcolonial literature?

One reason that Rohinton Mistry's novel is postcolonial derives from the author's position. He was born in India five years after independence. Mistry's heritage is Parsi, an ethnic and religious minority that suffered discrimination under British colonial rule. In the new nation of India, with a dominant Hindu majority, Parsi status did not significantly improve, leading to widespread flight. Mistry himself left for Canada.
Such a Long Journey gives a portrait of a Parsi family that remained in India and is now suffering the consequences after 25 years of independence. The protagonist, Gustad Noble, maintains a positive view of their situation despite reversals of fortune that have left them barely clinging to the middle class. His involvement with a humanitarian activist is connected to the plight of Bengalis, another minority in India, who have become refuges from the war with East Pakistan (on the verge of becoming Bangladesh).
The deep, reprehensible corruption that afflicts this noble cause unexpectedly intrudes into Noble's life. He is forced to question his assumptions about a man whose friendship he trusted: Major Bilimoris. The political dynamics of Mistry's questioning of the postcolonial status quo elevates the novel from a personally-oriented melodrama to a social critique. Not only Bilimoris but officials up through the nation's prime minister are implicated in the refugee assistance scam.
While the major pays for these schemes with his life, the higher-placed conspirators escape prosecution. Noble's family is torn apart and then put back together, somewhat the worse for wear—much like the Indian nation.

Postcolonial literature emphasizes "the view from below" or the point of view of the oppressed. Often it is written by people from countries with a long history of being oppressed by European colonial occupiers who came in and exploited the land and its people. However, more broadly, it can represent any view that depicts the lives of the oppressed. It counters the official, often rosy narrative of the dominant group with a different version of the story.
Mistry's novel, which takes place in India in the 1970s, fits the description of post-colonial because it tells its story from the point of view of oppressed Indians and outlines in detail the extreme poverty that existed in India. While it is not attacking an outside colonial power, it is criticizing a system that treats lower-class people with humiliation, imprisonment in a work camp, and torture. A character refers to a real-life political leader, Bal Thackery, as one who "worships Hitler and Mussolini." This depiction of a politician struck such a nerve in the ruling elite that the book was banned in 2010 from the University of Mumbai's reading list. Like other post-colonial literature, it brings to light aspects of society that the "official" version would rather keep quiet and explores the effects of poverty, cruelty, and injustice.