We are just now getting eggs from the chicks we got in the spring. Some of the eggs have what I would call a small flake or two in them. What is that. This hasn't stopped me from eating them but I am wondering what this is.

Eggs from just laying hens often have blood spots in them though that doesn't sound like what you're seeing. Some people who have never eaten a really fresh egg sometimes wonder about the little spot that, if the egg was fertile, would become the baby chick. It doesn't sould like that's what you're seeing either.
I find that if I look around I can usually find an answer to most of my chicken questions at www.feathersite.com
It can take a bit of clicking and following links but you might find an answer here.

sometimes pieces of chalazae ( the natural filaments that hold the yolk in suspension in the albumen (egg white) can be seen in the egg, especially from young hens. This is completely natural and not a quality or safety issue. Bloodspots can also appear, but they are usually red or dark brown. The small white circle on the yolk is the germinal disc which is the site of fertilization. It is much more prominent in fertilized eggs but is perfectly normal and not a problem.