Most export/import tools will not work. In fact, if you’re using the WP export/import it won’t do images correctly unless you export/import an entire site.
If you must export/import than the only suggestion I have is WP All Import/Export Pro versions that will work with ACF. You can create custom filters on the export to get images and format them correctly for the import and the import is aware of ACF fields and will import the content correctly.
I can’t help you more because I have never had a need to export/import, when I migrate a site it is always a complete site migration where I export/import the entire DB.
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users
Helping others is a great way to earn karma, gain badges and help ACF development!