The first thing to do with this question is to identify which theme (or themes) you are going to discuss in relation to dreams and omens. The Alchemist has more than one theme, and it won't necessarily work out to apply dreams and omens to every single one of the novel's potential themes.
One thing is certain: dreams and omens play a huge part in the novel. First, they function as a plot device, since it is Santiago's treasure dream in Egypt that reveals to him his Personal Legend and propels the plot forward. Another thing to take note of is how chasing and achieving your Personal Legend sounds very similar to when a person talks about "following their dream" to do something or be someone. Santiago is motivated to pursue his dream, his Personal Legend, at all costs.
The importance of Santiago's metaphorical dream is woven together with the importance of literal dreams in the novel as well. This extends beyond Santiago's own dream. The novel shows readers that there is a difference between believers in dreams and nonbelievers. The believers are enlightened people. They are "the good guys," and we see this in Santiago for sure, but we also see it in the chieftain who takes seriously Santiago's dream about the hawks. The novel weaves in stories of the biblical Joseph and his ability to interpret dreams and the good things that happened to him. Santiago is granted this same ability and correctly interprets a dream that helps him find the treasure. Dreams and omens appear throughout the story and show readers the theme that dreams are important.