As I understand it, this question is simply asking how the American dream can help us to achieve political freedom. I assume that the key is metaphor. If so, the American dream can help us to achieve political freedom because it leads us to emphasize our individuality.
To see how this is so, let us first define the American dream. One way to define this is to say that it is the hope that any person who lives in America can better themselves through dedication and hard work. We can all achieve personal improvement and a good degree of material wealth if we care enough to work hard.
One aspect of this dream is individuality. In this vision, we do not rely on someone else to tell us what to do. We work in our own way and we try to improve in the way that we think is best for us. This aspect of the dream can “unlock” political freedom. It can help us to feel that our own individual rights are of paramount importance. Once we feel that our rights are important, we will be much more likely to demand that the government should protect them.
In this way, holding on to the American dream can help us to achieve and keep political freedom and civil liberties.