Re-initializing a Duo device does not produce an entirely different string in the new QR code, so just in case I'm not going to post a real decoded string on a public list. However, I will attempt to describe what I see experimenting with this.
The three codes I have gotten so far are all mixed-case alpha-numeric strings 59 characters long, with a hyphen at character 21. The first 20 characters vary between QR codes. The 38 characters after the hyphen are constant even when Duo believes it is configuring different devices. I hope this means that the constant string is an account identifier of some kind rather than key material, but so far I can't be certain.
The Duo soft token application also clearly phones home to activate the toek after scanning a QR code, so it would be necessary to reverse engineer the phone-home protocol to make FreeOTP work with QR codes intended for the Duo app. According to their web site Duo allows for the use of HOTP tokens, so there's probably not much benefit to reverse engineering their proprietary token type.