Results are reported from an analysis of 80 000 pictures of 6.935-BeVc antiprotons in hydrogen leading to final states of the form K10+K10+m, m=0,1,2. Assuming equal probability for the various KK charged states, we find the cross section for the reaction p+pK+K+m to be 2.50.5 mb. A compilation of annihilation cross sections indicates that the kaonic-annihilation final states constitute approximately 10% of all annihilations from 1.6-7 BeVc. The production of K*(1400) has been observed, although the formation of other resonances such as K*(890), and is less copious at 7 BeVc than at 3.7 BeVc. A K10K10 enhancement near threshold is observed similar to that observed at lower-energy annihilation reactions.