Strengthening Fishing Communities and Increasing Flexibility in Fisheries Management Act This bill revises provisions related to fishery management activities and otherwise sets forth new requirements related to fisheries. The National Oceanic and Atmospheric Administration (NOAA) must publish every three years a plan to conduct stock assessments for any species subject to a fishery management plan. NOAA must also develop a plan for implementing cooperative research with fisherman and outside groups. The bill provides authority for fishery management councils to (1) use alternative fishery management measures in a recreational fishery (or the recreational component of a mixed-use fishery), (2) consider changes in an ecosystem and the economic needs of the fishing communities when establishing annual catch limits, and (3) base fishery stock rebuilding time frames on science given the biology and characteristics of such stock. The bill also 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.