McLemore was participating in a land navigation assignment on Wednesday. It was a military training class of the Basic Leader Course at Camp Blanding's 211th Regiment Regional Training Institute.
He was last seen around 11 a.m. and did not return, authorities said.
Canines, mounted patrol and the Jacksonville Sheriff's Office, helped Clay County Sheriff's Office search for McLemore.
Some of McLemore's equipment -- water, food, paperwork and a tool to navigate -- was located by search teams.
Cura McLemore told WHBQ that authorities told the family that he had died -- but not how.
“I want my brother back with me,” Cura McLemore said. “That's my best friend. The only friend I have.”
Shannon Mayes, McLemore’s cousin, said something isn’t sitting right with her, after they found out McLemore had a cell phone on him.
“Why he didn’t use that cell phone?” she said.
The family told WHBQ they suspect something is being covered up, because they cannot figure out why he wouldn't make any calls if he knew he was in danger.
“How can a cell phone go dead?” Mayes said. “You would have made a call when you feel like something is wrong.”
Nothing has indicated anything suspicious about McClure’s disappearance or that he's AWOL, authorities said.
Officials believe he may have become disoriented and dehydrated in the heat.