Elvis used a double-tied home-made string-strap on his first, then a light-brown leather tooled strap on his MartinD18, then, dark brown leather-tooled strap on his MartinD-28 and finally a lighter brown leather-tooled strap.
Although the exact brand of guitar strap Elvis used is unclear, photographs reveal that he often used a leather guitar strap which was tan with a pattern on one side. Apparently, when his usual strap couldn't be found prior to a concert he substituted a clothesline.
Elvis Presley used multiple types of guitar straps, but the most distinctive one that he used is a blue corduroy guitar strap with metal studs around the shoulder
Well with most of his guitars he used a leather strap. I believe you can purchase his original on auction but it is very expensive. Also to buy other leather straps visit ebay.
Other than a trivial notion, what the heck did it matter , what "guitar strap " he was using?
That's like asking , "um, what color of socks was Elvis wearing when he recorded Heartbreak Hotel"?