How do I get "get-iplayer" to use an already installed ffmpeg?
I would reccomend installing Homebrew and running brew install ffmpeg. That way you can delete the other one, because Homebrew installs it in /usr/local/bin so you won't have to worry about path issues.

To install from the source you've already got:
From this page:

cd ~/Downloads/ffmpeg to go to the FFMPEG directory

./configure along with your needed flags. You probably won't need anything additionally for what you're doing.

make and then sudo make install. Be sure to type your admin password.