AFI 36-2903 18 JULY 2011 Chapter 10-Badges and Specialty insignia (page 140/ 141)
10.5. Qualification and Miscellaneous Badges and Patches. Qualification badges are defined as badges earned and permanently awarded that reflect special skills that an Airman has demonstrated proficiency or qualification in that complements their primary mission. Wear of other services' qualification badges, if earned and awarded, is authorized. Award criteria for other services’ qualification badges will be in accordance with awarding Service’s directives (Army MilPERCEN; Navy; BUPERS, etc.).
"Qualification badges will be in accordance with awarding Service’s directives" this means they will be in the color Thread that the Navy, Army, USMC, Cost Guard tells us they will be in