I’d start by adding a hidden custom field that sets the date that gets set when the value of the chekbox is updated. You can set the value with an acf/save_post filter http://www.advancedcustomfields.com/resources/acfsave_post/ or maybe even an acf/update_value filter http://www.advancedcustomfields.com/resources/acfupdate_value/ and you can set another field with the date or date and time using update_post_meta() http://codex.wordpress.org/Function_Reference/update_post_meta.
Then I would look at learning how to set up a cron in WP https://codex.wordpress.org/Function_Reference/wp_cron
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