My son entered the program through the 7th grade talent search, so he got in on the basis of ACT scores, and the course he took was through the e-studies program. He had to qualify through the TIP program to be eligible to enroll.
According to the TIP website, the talent search programs for younger students require qualifying scores on a standardized test. The acceptable tests and scores are listed here:
http://www.tip.duke.edu/talent_searches/grades_4-5/enroll.htmlDuke also offers Independent Learning courses that anyone can order, with offerings from 4th grade on up.