I'd be interested to know how you've got on - I'm looking to use Fontawesome Pro 5, and it seems the inclusion of FA is really poorly implemented at the moment - the files are stored in /lib/fonts, but the stylesheet to be used has to be copied (and slightly modified) into the theme's styles subdirectory.
This stuff really needs to be pluggable as-is, to enable use of any version of FA (4, 5 or newer, free or pro) just by unpacking the FA download into the right place. Otherwise it's way too hard to use Pro, which is a pain for users and rude to the developers of FA itself.
Personally I'd like to see this (and bootstrap & other similar stuff) completely outside of themes - a plugin to install, which a theme can depend on if desired.