Phil Ford tells us why James Brown was so funky. (It's the rhythm, stupid!) On this post-Boxing Day evening I don't have much more to add, other than to suggest that timbre has something to do with it as well, from the chicken-scratch guitar that Phil describes to the percussive-melodic quality of JB's voice. The blurring of lines between melody and percussion through timbral miscues (for example, the percussive hits of the brass) move us to a different musical realm. Dare one call that realm "funk"?
Also see Scott McLemee's thoughts on the Godfather of Soul.