Is a vet an option?
It appears your drake has had a prolapse, which can happen for several reasons, but it's possible the tissue came out while he was mating.
It would be a good idea to move him inside and set him in towels where he can't further infect the tissue with debris. Is that feces, or something else surrounding the tissue? I would try to gently flush the area with some saline to lavage out any debris or fecal matter. Once it's been lavaged well, apply an ointment to keep the tissue moist like Neosporin, or Preparation H. Make sure the tissue stays moist, and if it doesn't shrink in by itself, which it may very well won't, you'll need to try to encourage the tissue back inside his body.