I recently bought a secondhand Flextone Line II and was experiencing problems with intermittent volume, delay etc. changes, so this evening I flashed my amp's flash memory from version 1 to 1.10. I don't know yet if it has improved matters, as I am reading up on issues on this website and now replying to your post, but anyhow this is what I did:-
I registered on Line6.com as a new user.
I already had the recommended M-audio midisport Uno interface so that part was sorted!
I would imagine most PCs need an external midi unit like the Uno to interface to the Flextone III.
The Uno has 3 leads: a USB lead to plug into the PC, a midi lead to plug into the Flextone Midi In socket, and a midi lead to plug into the Flextone Midi Out socket. The Midis are marked appropriately on the Uno plugs and above the Flextone sockets.
I installed the latest M-Audio drivers for my PC running Windows 7 SP1.
I hooked up the Uno's USB plug into the PC's USB port and checked it was now recognised (message temporarliy displayed in the PC display's bottom right tray).
I downloaded Line 6 monkey latest version and installed it as Administrator (right-click on .exe to see option).
I plugged the Uno midi lead saying 'To Midi In' on the plug into the Line 6 amp's Midi In socket.
I plugged the Uno midi lead saying 'To Midi Out' on the plug into the Line 6 amp's Midi Out socket.
I ran Line 6 monkey, which recognised the Flextone immediately.
I selected to update the Flash Memory.
It wanted me to register the product so I entered the serial number on the website (two or three different times), but got 'error 532 could not be validated'.
So I went back to Line 6 monkey and tried again, this time clicking 'Remind Me Later' (to register).
I did not bother backing up the patches in the next step.
Following this the flashing started and progressed smoothly (maybe 5 minutes) and the monkey program confirmed the flash memory is now the latest version 1.10.