I use Inkscape primarily as my primary vector editor. I'm on a mac.
As far as I can tell, there's no way to just get the vectors directly into Inkscape (you'd think opening up the svg font file would give you something but nope)
Installed the otf font (again I'm on a Mac, if on Windows try other font types if you don't like the otf).
Copy in all the characters as type.
Then "outline" them in Inkscape as you would turn any font into artwork.
This is how I got the vectors in Inkscape.
To be clear: After installing the latest Font Awesome font, I open up the Font Awesome "cheatsheet" page: http://fontawesome.io/cheatsheet/
I select the FontAwesome font as my font in Inkscape
I then copy the ICON itself from the the Font Awesome cheatsheet page and paste it into Inkscape as text.
Last, just "ungroup" the text selection until it becomes a pathed object.
You can then change/tweak the vectors.