Preventing Sexual Abuse of K-12 Students Act of 2019 This bill addresses sexual abuse of students in elementary and secondary grades (K-12). The bill requires states receiving federal education funds for elementary and secondary students to establish and implement a statewide policy requiring each local educational agency to (1) develop codes of conduct to prevent sexual abuse of students by identifying acceptable and unacceptable behavior for school personnel and students; and (2) ensure that school personnel receive specified training, including regarding sexual abuse and misconduct awareness and prevention. The bill authorizes funding for sexual abuse awareness training at the state and local levels under various programs, including (1) grants for state assessments, and (2) student support and academic enrichment grants.