ACF features an activity log that keeps track of all of your imports and exports of your custom fields, and is available on both the dashboard and just below in the export/import buttons in the fields overview:
The activity list shows both completed and currently running exports and imports along with their current status. The page refreshes automatically every two minutes but you can also click the refresh icon in the top right corner of the list of manually refresh the list.
In case of any import errors you will also be able to view them from the activity log.
It is also possible to download any files you have previously exported or imported in ACF making it easy to manage your activities.