Homebrew v2.0 dropped all of the extra options that are not explicitly enabled in each formulae. So the --with options no longer work if you use the core Homebrew formulae.

Instead you can use a third-party repository (or "tap") such as ​homebrew-ffmpeg. This tap was created in response to the removal of the options from the core formulae.

Enable it then install ffmpeg:

brew tap homebrew-ffmpeg/ffmpeg
brew install homebrew-ffmpeg/ffmpeg/ffmpeg --with-fdk-aac

You can see a list of additional options with:

brew options homebrew-ffmpeg/ffmpeg/ffmpeg

It's recommended to install a recent build from the git master branch. You can do so with the --HEAD option:

brew install homebrew-ffmpeg/ffmpeg/ffmpeg --with-fdk-aac --HEAD