We present observations of the Cepheus Flare obtained as part of the James Clerk Maxwell Telescope (JCMT) Gould Belt Legacy Survey (GBLS) with the SCUBA-2 instrument. We produce a catalogue of sources found by SCUBA-2, and separate these into starless cores and protostars. We determine masses and densities for each of our sources, using source temperatures determined by the Herschel Gould Belt Survey. We compare the properties of starless cores in four different molecular clouds: L1147/58, L1172/74, L1251 and L1228. We find that the core mass functions for each region typically show shallower-than-Salpeter behaviour. We find that L1147/58 and L1228 have a high ratio of starless cores to Class II protostars, while L1251 and L1174 have a low ratio, consistent with the latter regions being more active sites of current star formation, while the former are forming stars less actively. We determine that, if modelled as thermally-supported Bonnor-Ebert spheres, most of our cores have stable configurations accessible to them. We estimate the external pressures on our cores using archival 13 CO velocity dispersion measurements and find that our cores are typically pressure-confined, rather than gravitationally bound. We perform a virial analysis on our cores, and find that they typically cannot be supported against collapse by internal thermal energy alone, due primarily to the measured external pressures. This suggests that the dominant mode of internal support in starless cores in the Cepheus Flare is either non-thermal motions or internal magnetic fields.