Palmer was one of three pilots who flew this Learjet around the world, though they made many landings along the way including starting at Denver then stopping at Boston, MA, Glamorgan, Wales UK, Paris, France, Tehran, Iran, Colombo, Sir Lanka, Djakarta, Indonesia, Manila, Philippines, Wake Island, Honolulu, HI, and landing back at Denver. Palmer is listed in most of the publicity as the pilot and he has said that he was at the controls for much of the flight, but there were two other pilots there as well, James Bir and Lewis Purkey who were also at the controls for parts of the flight. In fact, Bir and Purkey were Learjet corporate pilots and knew the ins and outs of flying this particular Learjet 36 better than Palmer, but Palmer's name was the one that attracted the news crews since flying around the world was nothing new and had been done a great many times starting in 1924 and then somewhat regularly ever since. This 1976 flight by Bir, Purkey and Palmer set a speed record for a heavier than air land plane which is why it was flown.
I do not know how many covers were flown and how many were autographed by Palmer, Bir, or Purkey, but my guess would be that there would have been a significant number since weight would not have been an issue for this aircraft and given that it was landing so frequently for fuel and servicing. Also, I would guess that Palmer signed a great many of them while finding autographs of Bir and Purkey may be more difficult. By comparison, the 1986 round the world flight by pilots Rutan and Yeager which also carried covers that were autographed by both of them were limited since the record they were setting had to do with being the first "non-stop round the world land aircraft" and they had to weigh every ounce to make it. Note all of the limiting words such as Land aircraft which excludes things like the Graf Zeppelin which flew around the world with 64 passengers and crew and while it stopped at 5 cities it never actually completely touched down at them.
As for value for your 1976 record time flight I am not certain what you might get for it, though my guess is that it may not be as much as what some people might hope. It is not very old, the feat was not very difficult, and there was not very much publicity about it so there is limited demand among a small number of potential collectors since most first flight cover collectors tend to seek the older material from before WW2. One approach might be to put it on
ebay for $50 and see what happens and if there are no bids then drop the opening bid to $25, and if still no opening bids then drop it to $10 and see what happens. Or what I personally would do it do it the other way around and put it on
ebay with a starting bid of $1 and see where the auction mechanism takes it.