This was discussed on the DZ last year, but it was left unresolved. That is, the question of Cooper and the chutes from McChord.
Himmelsbach claims that DBC specifically requested the chutes come from McChord. Contemporaneous news articles at the time say Cooper was offered chutes from McChord and rejected them for an unknown reason. Some sources say he rejected the military chutes and demanded sport chutes. The 302s only mention the Hayden/Cossey/Emerick chutes.
We know he ultimately ended up with two Navy rigs - McChord is/was an air force base. Fort Lewis did not have a paratrooper unit deployed there and paratroopers use static line - impossible for a jump from a commercial jetliner. I would assume the USAF would have bailout rigs, but my understanding is that they are almost universally automatic deployment and not manual ripcord. As R99 has pointed out, most military rigs contained beepers or pingers to locate the personnel attached to them.
So, what's the deal here? Did Cooper want chutes from McChord or not? If he didn't want military chutes, then why did he jump with one? And what about Cooper's complaint that "McChord is only a 20 minute drive"? If he was expecting the chutes from McChord, then why reject them? Were there two chute deliveries? Can anyone make sense of the McChord Chute Stuff?
Chaucer, military paratroopers were doing free fall (HALO - High Altitude Low Opening) jumps from at least the mid-1960s. I saw military paratroopers demonstrating this about 1964 or 1965.
If the missing Hayden parachute is similar to the one he donated to the WSHM, then he did not have a Navy parachute. The WSHM/Hayden parachute appears to have been assembled by Cossey from multiple sources for various rigs and not one particular design.
In Vietnam, the military parachutes did have pingers which everyone with suitable radio equipment, including the bad guys, could home in on. Today's military pilots have access to personal equipment devices that includes two-way voice communications, GPS locations, etc., all of which can be transmitted enciphered.
Generally speaking, today's military emergency parachutes involve free falling to about 14,000 feet where the parachute will automatically open. If the ejection is below 14,000 feet, the parachute will open immediately. The pilot can also pull the ripcord which will override the automatic system.