Fluke Fairness Act of 2019 This bill directs the Mid-Atlantic Fishery Management Council to submit for approval by the Department of Commerce a modified fishery management plan for the commercial and recreational management of summer flounder, or an amendment to the plan, that is based on the best scientific information available; establishes commercial quotas in direct proportion to the distribution, abundance, and location of summer flounder as reflected by fishery independent surveys conducted by the National Marine Fisheries Service and state agencies; considers regional, coastwide, or other management measures that comply with national standards under the Magnuson-Stevens Fishery Conservation and Management Act; and prohibits the establishment of commercial catch quotas on a state-by-state basis using historical landings data that does not reflect the status of the summer flounder stock, based on the most recent scientific information. Commerce must prepare and consider a plan if the council fails to submit the modifications or amendments. The Government Accountability Office must assess and report on whether the subsequent implementation of the approved plan or amendment complies with national standards.