Amazon do NOT know my date of birth. And you REALLY don't want to ask. If you ask, some people might be stupid enough to tell you -- you then have an important piece of personal information which you need to keep secure or risk legal repurcusions if you lose it!
If you need to know if someone is over 13, ask them to declare that they are over 13.
If your lawyer tells you you actually need to know people's age, then ask them their age. Do not ask them for their date of birth, which is a much more sensitive piece of information (many real-world identity checks include date of birth).
Thanks for the input Graham. Unfortunately I'm the lawyer, and one of the experts in the field believe it or not. I'm not going to get into the particulars of COPPA in a forum post, but your points are well taken, and I'll see what we can do to change how we do that particular bit of compliance.