The purpose of Richard Rodriguez's story not being in chronological order is simple. Rodriguez simply is following how memories come to the forefront of the mind.
Memories do not exist as chronological events. Instead, they come on through triggers of the past. For example, think about walking into a room where you smell something familiar. Once your brain recognizes the smell, the brain triggers memories which align with the smell. Therefore, Rodriguez is recalling memories as they trigger specific events from his childhood and how the events align with his retelling of his recollections.
For most authors, when telling of autobiographical events, the retelling tends to happen chronologically. For Rodriguez, his story does not need to be told chronologically. Instead, the purpose of his story is to retell the events which led him to come to the conclusions that he does.
Rodriguez offers small pieces of his childhood which have impacted his current way of thinking. Therefore, chronology is unimportant. What is important is the fact of what he is trying to say to the reader.