Strengthening Fishing Communities and Increasing Flexibility in Fisheries Management Act This bill modifies provisions related to fishery management activities. Among other things, the bill authorizes fishery management councils to use alternative measures as part of management plans at recreational fisheries and for recreational portions of mixed-use fisheries; revises the annual catch limit requirements, including by allowing councils to consider changes in an ecosystem changes and the economic needs of the fishing communities when establishing limits; directs the National Oceanic and Atmospheric Administration (NOAA) to publish every three years a plan to conduct stock assessments for any species subject to a fishery management plan; requires NOAA to develop a plan for implementing cooperative research with fisherman and outside groups; prohibits feeding sharks in federal waters off the coast of Florida; and sets forth requirements under which a state may encourage the elimination of lionfish.