One of the values of the American Dream is freedom, and this is perhaps the value most explored in the film, Fear & Loathing in Las Vegas, in regard to the protagonist, Duke. This is because Duke essentially does whatever he wants without thinking, and this includes taking heavy amounts of drugs and causing chaos in his hotel room. The fact that he is able to do all these things reveals that he has personal freedom; in other countries, he most likely would not have been able to get away with all of these various antics.
At the same time, we also see other characters on the periphery of the film that reveal how a culture of excess and drugs can cause social breakdown. For instance, the girl they meet on the plane obviously comes from a broken home, and we also see the despondent looks of people gambling away their money at the casinos. What this reinforces about the American Dream is the idea of personal freedom to do whatever we want, although it does not necessarily support that we will always make good decisions. Freedom is the ability to choose our actions, and this includes the freedom to engage in self-destructive behavior. Not all of these behaviors are legal, such as taking illicit drugs; however, these behaviors are still possible and achievable, meaning that if someone in the US is intent on finding and abusing drugs, that person may very well succeed at this goal even though it would technically be illegal.
If we view the film as a social commentary, however, we can also see how the American Dream has failed society to an extent in the film, because beneath all the chaos being shown on the screen, there is a sense of unhappiness in the characters because each of them seem to be lost and without hope, or completely unconcerned with what happens to themselves or others.