This is a good question. It is probably best to start off with an understanding of postmodernism, so that we are on the same page. Postmodernism can be described as an intellectual movement that acknowledges the lack of a dominant narrative. Hence, there is an understanding that all knowledge is relative and based on a person's historical context and experience.
When we approach the works of Stephen King, we can say that this definition fits him well in three ways.
First, by Stephen King's very historical context, we can say that the air that breathes is postmodernism. He was born in 1947. Postmoderism was it the heyday in his university years.
Second, we can say that the breadth of his works, which span all different genres and styles is also indicative of postmodernism. For example, his book, Carrie is very different than The Green Mile and Hearts in Atlantis. This freedom or fragmentation or the lack of center of his works is very postmodern.
Third, there is also a strong anti-conformist and anti-authority point of view, which is also part of postmodernism. For example, in the Green Mile.The protagonist breaks every stereotype.