More commonly called Joint Service Order. This is for troop formations. For colors, the academy flags are displayed/carried after the parent service departmental.
The following is from DoD Directive 1005.8 (1977) with memorandum update (2016)
3.1. Cadets, United States Military Academy.
3.2. Midshipmen, United States Naval Academy.
3.3. Cadets, United States Air Force Academy.
3.4. Cadets, United States Coast Guard Academy.
3.5. Midshipmen, United States Merchant Marine Academy.
3.6. United States Army.
3.7. United States Marine Corps.
3.8. United States Navy.
3.9. United States Air Force.
(Most likely the United States Space Force will be here)
3.10. United States Coast Guard.
3.11. Army National Guard of the United States.
3.12. Army Reserve.
3.13. Marine Corps Reserve.
3.14. Naval Reserve.
3.15. Air National Guard of the United States.
3.16. Air Force Reserve.
3.17. Coast Guard Reserve.
3.18. Other training organizations of the Army, Marine Corps, Navy, Air Force, (Space Force,) and Coast Guard, in that order, respectively.
Provided, however, that during any period when the United States Coast Guard shall operate as part of the United States Navy, the Cadets, United States Coast Guard Academy, the United States Coast Guard, and the Coast Guard Reserve, shall take precedence, respectively, next after the Midshipmen, United States Naval Academy, the United States Navy, and the Naval Reserve.