You need to install and enable the Windows Upgrade Advisor application in order to perform the update. After that, the update is available for download through the standard Check for Update option in the Phone Update menu.
The release build of the new OS version for AT&T Lumia 640 XL is 10.0.14393.321.
AT&T Windows 10 Mobile updates
After several months of waiting, all AT&T eligible devices finally have access to the Windows 10 Mobile Anniversary Update. The Lumia 640 XL is the last eligble AT&T Windows Phone to get this major OS update.
While Microsoft and AT&T are working together on the Windows 10 transition, usually it is up to the carrier to release the update. So far, there are no details on why it took so long for AT&T to release the update.
The Windows 10 Anniversary Update aka Windows 10 Summer Update was rolled out to Windows 10 PC, HoloLens, and Xbox on August 2. Windows Phone owners had to wait two weeks longer until the first devices received the update also for Windows 10 Mobile.