Final answer:
The DEA, often working with the FDA, has the authority to add, delete, or reschedule substances under the Federal Controlled Substances Act. Congress can also influence scheduling through legislation.
Step-by-step explanation:
The entity that has the authority to add, delete, or reschedule substances under the Federal Controlled Substances Act (FLCSA) is The Drug Enforcement Administration (DEA), often in conjunction with the Food and Drug Administration (FDA). The DEA is responsible for regulating the use of controlled substances in the United States, including prescription drugs, illegal drugs, and other substances with a potential for abuse. The process typically involves scientific and medical evaluations by the FDA and a review of all available data by the DEA before a final decision is made regarding the scheduling of a substance.
Additionally, Congress may also pass legislation to control the scheduling of substances. It is important to note that while violations of standards for a given substance category can be addressed through various means granted by legislation to the FDA, the rescheduling specifically falls under the DEA's purview.