CLEP and DSST exams can be taken at any age. High school students take them to build college credit early. Adults take them to accelerate their degree programs. People of all ages returning to school take them to fill prerequisite or general education requirements.
Students as young as nine have passed CLEP exams. However, because scores expire after 20 years and colleges often change the configuration of test/score they accept, it is a good idea to wait until high school to start testing. Twenty years sounds like a long time, but it's not. If some of those scores are needed later on for graduate school prerequisites, will they still apply? They will need to be less than 20 years old. Sometimes it's that long before students decide to go to graduate school.