Star Trek actually stole NASA's design (both the Pantone colors and the lopsided arrowhead, which was the cambered, swept supersonic arrowhead wing that Modelli saw at Ames and Langley and added to the version he adapted from Harry DeVoto's 1958 NASA seal design), not USSF's. USSF uses parts of NASA's design (the orbit and star patterns) and parts of the AFSPC seal design, which derives from heraldic military symbols used on patches and seals long before Star Trek was even a book idea.
Star Trek actually stole NASA's design (both the Pantone colors and the lopsided arrowhead, which was the cambered, swept supersonic arrowhead wing that Modelli saw at Ames and Langley and added to the version he adapted from Harry DeVoto's 1958 NASA seal design), not USSF's. USSF uses parts of NASA's design (the orbit and star patterns) and parts of the AFSPC seal design, which derives from heraldic military symbols used on patches and seals long before Star Trek was even a book idea.