Chris Corinthian's framework for minimizing student loan debt involves using tools like the Common App, College Board Scholarship Search, Scholly, and Google to discover scholarships tailored to one's interests and deadlines. He suggests students take advantage of local resources, such as alumni associations, to find scholarships that are often less competitive for local applicants. Chris also emphasizes the importance of continuously applying for scholarships throughout college, not just in high school, to maintain financial support and minimize the need for loans.