Flesh Death's Heads are red variants of regular Death's Heads added to the Afterbirth DLC.
Their appearance look identical to normal Death's Heads with the exception of red colors, a different-styled mouth, and red pupils.
Just like the Dank Death's Head, they're vulnerable.
Isaac has a choice of either killing the Flesh Death's Head first in order to clear the room or not. Although, if there are monsters in the room along with Flesh Death's Heads, it will be better to kill other monsters first to clear the room because killing the Flesh Death's Head first is just wasting time or slightly increases a chance to deal damage.
On death or upon clearing the room, they explode into 6 directional shots.