From:
Alan Paul: 'One Way Out - The Inside History Of The Allman Brothers Band', pages 58 & 59 (St. Martin's Press, 2014):

STEPHEN PALEY, photographer who took the pictures on the debut album cover:
I had shot Duane a few times for Atlantic and got along with him really well, and the label hired me to shoot the cover for the first Allman Brothers Band album. I went down to Macon and hung out for about a week. I never liked a band more. I was one of them. I hung out with them, they got me girls, they gave me drugs. It was like being a rock star. I hung out with a lot of rock stars but no one ever did that to the same extent. There was just an ease to the whole thing. They really were the kindest, most fun band I ever worked with.
We spent a few days going all over Macon and shooting anywhere that looked photogenic: fields, old houses, railroad tracks, the cemetery. We shot a lot. They looked scary but they were sweethearts and they would do anything. I even went with Duane when he had oral surgery and shot him there—and, of course, they posed full-frontal naked! That wasn’t my idea. I would not have had the guts to propose it. It was Phil Walden’s idea. They trusted him and he said to do it, so they did. [Rolling Stone editor/publisher] Jann Wenner happened to be there, with Boz Scaggs, who he was producing. We were outside near a brook on Phil’s brother’s property and it just seemed like a natural thing to do.

On February 25, 2021 we contacted Stephen Paley and asked if he had more information about the 1969 photo shoot.
This is what he told us:
"Twiggs [Lyndon] was around and shooting pictures over my shoulder while I was shooting the pictures I was hired to take. Twiggs was there primarily to help me and the band, which he did magnificently, but it was my session for which I was hired by the record company to shoot. At the time the pictures were not specifically done to be the cover, that was an afterthought apparently."
"I have been to Macon to shoot pictures on more than one occasion. It was so long ago, others recall the dates better than I do. I am also 78 about to be 79 in March and old age is catching up with me...finally."

Stephen Paley

More photos taken at the oral surgeon:

The liner notes of the 1969 LP release show that the cover photos were taken by Stephen Paley.
Some of these photos are dated as Spring / May 1969, but the album was not recorded until August 1969.
It is also possible that the photos were taken in August 1969, when, according to Alan Paul's book, Stephen Paley also took the picture at the oral surgeon.

From Wikipedia:
https://en.wikipedia.org/wiki/The_Allman_Brothers_Band_(album)#Artwork :
The cover for the album was taken by photographer Stephen Paley. Paley had gotten to know Duane Allman during photo shoots for Atlantic. Paley stayed for "about a week" in Macon with the band, partying with the group. They approached any areas about the town that appeared photogenic, such as "fields, old houses, railroad tracks, and the cemetery." The front album cover photo was taken at the entrance of the College House (now owned by Mercer University) next door at 315 College Street. The back cover photo of the album was taken at the Bond Tomb at Rose Hill Cemetery, located at 1091 Riverside Drive in Macon.

The gatefold cover of the vinyl LP features the band posing nude in a brook. The shot was original manager Phil Walden's idea, and the brook was on his brother Alan's property. Alan later recalled, "The [inner sleeve] photo was taken in Round Oak, Georgia, down behind my log cabin there, which is also the back of Otis Redding's Big O Ranch". Rolling Stone editor Jann Wenner was present with Boz Scaggs, whom he was producing at the time. They brought bubbles to cover themselves up, but the bubbles were washed away by the stream. Trucks had sliced his leg open earlier that day, requiring thirteen stitches, and was unable to get in the water; he is standing behind Oakley in the shot. Walden suggested the band take a few shots standing full-frontal; the band was reluctant but he assured them they would never see the light of day. At their first performance at the Fillmore East that December, Trucks discovered the full-frontal shots were printed in a broadsheet alternative newspaper.

Paley later said of the cover shoot, "I never liked a band more. I was one of them. It was like being a rock star. I hung out with a lot of rock stars but no one ever did that to the same extent. There was just an ease to the whole thing. They really were the kindest, most fun band I ever worked with."