Some of my store bought radishes get grey/black in the white flesh when I cut them open. Any ideas why?

Your radishes are likely to have come from plants suffering black root rot/disease, or possibly one of the mildew diseases that can afflict radishes. It happens when they are growing, usually a result of a temperature and moisture problem. I would return them to the store and ask for a refund, because you certainly don't want to eat them.

Thinking by analogy - black spots in potatoes are caused by bruising, and as radishes are also root vegetables, maybe the same for them.
One extension service (Wyoming) says not to use radishes with black spots but doesn't say why.
Maybe other members will have more information.