Why did Frederick Douglass use his own life experiences in the narrative?
There are a couple of points to address in your question. I think that one of the first points is that Douglass has to use his own life as the narrative for the simple reason that Douglass wants to demonstrate how horrific slavery really is. The only way that he is going to be able to do this is by being able to use experiences from his own life, recollections from his own notion of slavery to bring out to the reader what it actually is like to be a slave. Douglass has a primary purpose of bringing out an intense feeling of hatred for the institution of slavery in the reader. Recall the words of abolitionist William Lloyd Garrison when he heard Douglass talk about his experiences, the basis of his narrative:
I think that I never hated slavery so intensely as at that moment.
When Garrison hears of what Douglass had to endure and was subjected to as a slave, it arouses an immediacy in reaction. For this, Douglass has to use his own life. He cannot present an economic study of exploitation or collect narratives from those "who know of a person who knows of a slave." Instead, he uses his own life. Through this, there is an immediate connection.
I think that another reason why Douglass uses his own life is for the purpose of empowerment. Douglass aims his message at those whom he wants to enlist in the fight against slavery. Yet, he also wishes to serve as an example to other slaves who suffer the same ordeal that he did. He wishes to broaden solidarity out so that there can be a shared form of resistance and eventual change to the condition of slavery that is locking out people of color from living the lives that Douglass feels they so richly deserve. We see this tendency to broaden his struggle to the predicaments of others in chapter 10, when Douglass teaches Freeland's two slaves how to read and write. Douglass does not see his struggle as "his" own solely. Rather, he sees it as an opportunity for others to learn from and with him and achieve their own liberation as he has. In this, Douglass uses his own life as an example to others.