Assuming the audio in the avi is good, you can use Vdub to remove it from the avi. (Direct Stream copy under Audio and hit File, Save Wav…)
You can convert the wav file to ac3 using ffmeggui http://www.videohelp.com/tools/ffmpegGUI
Now, when you try again with DVDFlick, use this ac3 file as your audio stream.
Or you can reauthor the existing dvd you have now and remove the bad audio and replace it with this ac3 file. I use DVDLab Pro as my authoring program and I know I can do this process with it. It is not free but a fully functional trial is available, and the help file is excellent. When you import the dvd into Lab Pro, let it demux into elementary streams. Delete the existing audio and import the new one you made in Vdub. Rebuild the dvd, with or without menus, chapter points etc. However you want to do it.
There is at least one more method to try, but I’ll save it for later.