I HAVE DONE THIS CHALLENGE!!! LISTEN UP!!
First thing and really the only thing i feel you need to do is to tear all the chicken off the bones of the wing then consume the chicken, that way, like someone stated before you can shove smaller pieces of chicken into your mouth, thus avoiding the sauce getting on your lips. You can also eliminate some of the sauce that way.
When i did it, i actually ate all 11 wings in 7 minutes, but i threw up immediately after.
good luck man, this is a bitch of a challenge.