Tried the adult meals last summer when KLM wasn't offering any special meals and no choices for anyone, they wouldn't eat one bite! Usually the kids meal has a hamburger or pizza that looks gross, but they eat it.

Update: I called Delta again and the agent was much more helpful than before. She immediately contacted the SkyTeam desk and they identified the problem. Kids' tickets were in fact issued as "adults" even though there is only one way to book award tickets on the Delta website. They reissued the tickets a different way, and then the child's meal option suddenly appeared when browsing special meals under My Trips on klm.com.

It's odd they would code a child's ticket as an adult ticket when the DOB clearly indicates otherwise. But problem solved.