From Wikipedia

"....it is unclear if a two-term President could later be elected—or appointed—Vice President. Some argue[who?] that the Twenty-second Amendment and Twelfth Amendment bar any two-term President from later serving as Vice President as well as from succeeding to the presidency from any point in the United States Presidential line of succession. Others contend[who?] that while a two-term President is ineligible to be elected or appointed to the office of Vice President, he or she could succeed from a lower position in the line of succession which he or she is not excluded from holding. Others contend[who?] that the Twelfth Amendment concerns qualification for service, while the Twenty-second Amendment concerns qualifications for election. Neither theory has ever been tested, as no former President has ever sought the Vice Presidency, and thus, the courts have never had an opportunity to decide the question."