Veterans Education Flexibility Act This bill declares that, if an individual eligible for educational assistance under the all-volunteer force educational assistance program of the Department of Veterans Affairs is enrolled in an educational institution and the period of entitlement (10 years after discharge or release from active duty) would expire during a quarter or semester of enrollment, the period shall be extended to the end of that period (or until the earlier of the end of the course or 12 weeks in the case of an educational institution not regularly operated on a quarter or semester basis). The bill: (1) repeals the delimiting period for the use of assistance under the post-Vietnam era veterans' educational assistance program (generally 10 years after the veteran's last discharge or release from active duty), and (2) applies the assistance extension provided under the all-volunteer force educational assistance program to the post-9/11 veterans' educational assistance program.