Ms. Nurdan Yavuzalp, of the BSEC Permanent International Secretariat, very kindly provided me with an image of the flag of BSEC and a brief description of its symbolism.
The flag is white on pure blue and shows the BSEC oval logotype in its centre, with the organization's usual name across the top ("Black Sea Economic Cooperation") and triple stylized waves across the bottom. The blue field represents the Black Sea, and the wavy lines under the logotype reinforce the symbolism by representing the Black Sea's waves (besides balancing the composition). The proportions are 2:3. The flag is not specifically defined by the Organization's charter and seems to be an ad hoc design.
The logotype seen on the flag is a little different from the one seen on the BSEC website; the former is italic sans serif, whilst the latter is normal serif.