You should take a look at the acf/pre_save_post hook along with the information on acf_form, although I’m not familiar with submitting to mailchimp. You’d need to get the values submitted through the acf_form and then construct the values you want to send to the API in your pre_save_post function.
http://www.advancedcustomfields.com/resources/acf-pre_save_post/
http://www.advancedcustomfields.com/resources/acf_form/