Sharepoint to approval flow

I haven't checked in a while, but as far as i know a flow runs 'after' the list item is modified/created, therefore you can't check if the Employee ID was null to start with.

I would create a hidden text field to copy the Employee ID 'after' the approval has been approved.
Your flow can then use the 'When an item is created or modified' with a condition to only send for approval if the EmployeeIDCopy is null. Then add a 'modify item' if it is approved to copy the EmployeeID to the EmployeeIDCopy field else don't copy if not approved. Hope the makes sense!