You don’t need to sync them. The JSON files will be used everywhere except for editing them. If no one is going to edit these field groups on any of the other sites then syncing can be ignored.
If I was going to do something similar, this is what I would do, however, parts of the sites may not work during the process, so it really depends on how many of these sites you have.
STEP 0 – BACK UP YOUR DATABASE
1) I would go into all of the other sites (all of the sites except the main site where you plan on editing these field groups) and I would delete all of the field groups from ACF. This will also cause your JSON files to be deleted, meaning that the fields will not appear on these sites until you do step 2
2) Go back into the main site where you want to edit the groups and update each field group so that the JSON file is re-saved.
With that done you will have only one place where you can edit fields and those fields will be used on all sites using the same theme.
