Import FFmpeg into Audacity
The more or less official source for FFmpeg Windows Builds is here: http://ffmpeg.zeranoe.com/builds/
On that page, select “Shared” so the DLL will actually be there. It will be located in the “bin” folder. However, the current version is 57. It may or may not work with Audacity.
Also keep in mind to pick the correct choice from 32/64 bit: It needs to match Audacity’s “bitness”. You can look in Task Manager to find out whether it’s a 32-bit process.
On the official Audacity wiki, theres a section on how to get FFmpeg. It directs you to this page: http://lame.buanzo.org/#lamewindl You can find the required FFmpeg version there.
Downloads from that page are terribly slow, so I’ll provide a mirror: http://download.futuretech.in/ffmpeg-win-2.2.2.zip
Unfortunately, there’s no checksum on the original page, so I cannot prove that my mirror isn’t tampered with. Use it at your own risk.
As of January 2021, the official Audacity manuals' instructions for Installing FFmpeg for Windows advise downloading FFmpeg from lame.buanzo.org; scroll down the page and click the link "FFmpeg RECOMMENDED ZIP OPTION: ffmpeg-win-2.2.2.zip", unzip it in your desired location, then point Audacity to avformat-55.dll in the unzipped folder.