Shark Fin Sales Elimination Act of 2019 This bill addresses the sale of shark fins and the inclusion of rays and skates in the Seafood Traceability Program. (The Seafood Traceability Program has data reporting and recordkeeping requirements at the time of entry for imported fish or fish products entered into U.S. commerce.) The bill makes it illegal to possess, buy, or sell shark fins or any product containing shark fins, except for certain dogfish fins. A person may possess a shark fin that was lawfully taken consistent with a license or permit under certain circumstances. Penalties are imposed for violations under the Magnuson-Stevens Fishery Conservation and Management Act. The Department of Commerce must revise its regulations to include rays and skates as species that are subject to the Seafood Traceability Program.