Never had any with blackhead, but if they have been house with chicken. My guess the chicken may be carriers. Reason I never house chicken with any of my peafowl. If you do have a chicken that is a carrier , it will not harm the chicken ,but spread blackhead to peafowl or turkey.
So treat the chicken you have also.
Myself I never take the risk, guess risk not bad when you only have a few, but my number of past peafowl . A few chicken could cost me thousands