Prior to 1938, each borough had its own awards program. Brooklyn moved many of the awards that could be earned at their Kanohwahke Scout Camps located at Bear Mountain Parks in NY to Ten Mile River. The primary award was the Teepee and Canoe a series of three degrees earned by campers by completing various requirements.
The first degree was the Teepee with a B for Brooklyn in the camp colors Khaki and Maroon.
Here is a sample of the requirements from the 1929 Camp Guide.
the images are for the Second and Third Degree patches.
The versions from Kanohwahke Scout Camps had a different color scheme orange and black, still looking for those.
Let me know if you have any for trade or sale.