Today we have observed for one of the users in CRM Import Data button was not visible.
We did check the security role and I feel that all the security role were given properly. Normally for users who have the base role we don’t give delete permission on any entity.
Here is the link which explains the basic permissions needed for importing data into CRM.
Basic Security Role Privilege for Data Import in CRM
After some search came to know that we need to give User level Delete Privilege on Data Import and Data Map. This is the minimum delete privilege to be given in order to Import data into CRM where Record Deletion is not entertained.
After making below change, Import Data button is shown on the ribbon.
Set the Privilege at the user level first and then move to the Organization level as per the requirement.
Hope this helps.