The flag is reported in the League of Nations Official Journal in a report by the Straits Commission. The Straits Commission was an international body set up by the Straits Convention, a part of the Treaty of Lausanne peace settlement, to regulate navigation through the Dardanelles and Bosporus. The eight man Commission started its work in October 1924 and continued to function until Turkey regained full control over the Straits by the Montreux Convention signed in 1936.
Towards the end of the "First Report by the Straits Commission for the Year 1925", published in League of Nations Official Journal, Vol. 7, 1926, p. 957, mention is made of a flag. The Commission writes: "The Commission thought it might be desirable for it to possess a flag of its own, like the two International Danube Commissions, to designate its headquarters, and, if necessary indicate the presence of its members when on an official mission in the Straits. It therefore adopted a model flag (two gold tridents crossed on a dark blue field), the designing of which the President and Turkish Delegate himself undertook to have carried out." The report then goes on to describe a "flag incident" arising from the Turkish government's objection to the raising of the flag, a position which was headed by the Commission's President and the local staff. However, the report also states that the Commission passed a vote of censure against the president because the flag had been adopted by correct procedure. The report does not say anything further about the use of the flag, nor are details as to the design of the tridents revealed. I have made an attempt at drawing the "model" flag to be considered as a tentative recreation until we have further evidence.
What appears to be a contemporary drawing of this flag can be found in the German navy Flaggenbuch (1926). In this book the flag is labelled Meerengenkommission. The proportions of the flag as drawn in the Flaggenbuch (1926) are approximately 3:4.