The contract or procurement specialist should look in the reference guide "DEPARTMENT OF DEFENSE GOVERNMENT CHARGE CARD GUIDEBOOK FOR ESTABLISHING AND MANAGING PURCHASE, TRAVEL, AND FUEL CARD PROGRAMS Effective 1 October 2017".
IAW guidance on page 33 of this document, paragraph (G), indicates procedures for procuring "badges and insignia" as an example of an assigned commodity. Patches for use by participants (pilots) during an official function such as an Air Show would be allowed. However, purchasing patches to give to local dignitaries or visitors is not allowed.
Also see related DAU AAP GPC Purcahse of Special Patches: https://www.dau.edu/aap/Pages/home.aspx#!details|18121