Not sure how I got on this old thread, but it seems like the basic followup question was not ever explicitly answered here:
As Elliot points out “ACF saves it’s values in the native wp_postmeta table” for fields that are attached to a post.
Likewise, ACF leverages the core wordpress functions and tables for storing options – so they are found in the wp_options table. Any migration tool that migrates your entire install should move these options just fine.
If you want to migrate a few options values, you might want to checkout the WP CLI option command.
