There are several ways to compile FFmpeg. Homebrew is an easy way to compile FFmpeg files but sadly they are not static.
Static means you can copy the FFmpeg file anywere you want. It has no dependencies compared to a dynamically build like Homebrew does.
The below script will build a real static FFmpeg file. It does not cover all possible external libraries but it will give you a headstart. You can of course add more libs like Theora, Vorbis, VPX, .. yourself.