However, a swimmer that doesn't execute the movement correctly will probably increase the risks of *pain* (note I avoid the word injury, although one can lead to the other).
Butterfly kicking action while restricting body ondulation (holding the board, blocking the upperbody) can be technically quite difficult to achieve.
On the other hand, fly kicking no board with emphasis put on body ondulation is so good for perfecting the butterfly that (to me) it should be favor over kicking with a board.
I am a BF swimmer, and I never use boards. I am faster without than with a board anyway. Without board, my bf kicking is my fastest kicking action, and by quite far.