"Ils mangent mon poulet noir."
It cannot sound something incorrect: the only other version acceptable is : il mange (no 's' mon poulet noir (masculine, no 'e')
"il mange" and "ils mangent" are pronounced exactly the same way. That is why "he eats" and "they eat" are valid translations.
It doesn't have to mean burned chicken.There is a certain type of chicken which is called Black Chicken or Silkie. http://www.slashfood.com/2010/10/20/cooking-on-the-dark-side-black-chicken/