First, I'm sorry for your loss.
I'm a little confused about your description. Was there blood on the outside of the chick's neck, or inside in its throat? If the blood was on the outside, it may have been attacked by the other birds or other animals. If the blood was in its mouth/throat, that may have been due to normal death proceedings, or due to something that it swallowed.
Unfortunately, sudden deaths are not rare in chickens and often the cause is never determined. Your chick could have had a heart attack or an internal, genetic deformity that led to its death. Without a necropsy or more distinct symptoms, we may never know what killed it.
The hens' food (presumably layer feed) would not, in my opinion, cause a sudden death like this. Layer feed is mostly a problem due to its higher calcium levels, which can be hard on a young, non-laying bird's body. However, if high calcium was the problem, I would have expected the dead chick to have showed increasingly severe symptoms, not simply have turned up dead with blood on its throat.
For now, I would watch your other birds for other symptoms and continue to provide them with fresh water, quality feed, and a safe environment. Hopefully this death was just a fluke.