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:

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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.