Hey hey,
Thanks for posting! In order to add a birthday field to your plugin's form, you'll first want to ensure that you've added a birthday field to your MailChimp list, inside of your MailChimp account.
If you haven't created one yet, you'll want to log in and go to the Lists tab > click the arrow beside the list in question and click "Signup Forms". From there, click on General Forms and use the "add a field" buttons on the right-hand side. You should see that Birthday field is one of those options.
Once you've added that Birthday field, you'll then want to log back into your Wordpress admin area and go to your plugin's settings. Then, click the "update list" button at the top, where you should then see that the birthday field is recognized by the plugin for you to add it to your form if you choose.
If you have any questions about this process, feel free to post back here and we'd be happy to help! (btw, the site looks awesome and I'm very hungry now.)
-tk