Hi Ben,
Third-Party tools such as Kingswaysoft connect to the systems via a Dynamics CRM user account, and so the permissions that would be required would have to be added to the user account you are using.
In general, if you are just testing out the connections to make sure everything can work, the recommendation is to use the System Administrator security role since it has full access to all tables.
Once you confirm that you can connect and do your updates, you will need to identify what tables you are updating and apply a security role (or create a new one) that has the proper permissions.
For example, if you are updating the Contact table you would want to have Organization-level permissions for the Read action for the Contact table. If you are creating any records, that permission would have to be extended to the Create privilege.
Once you identify the tables you are updating/creating, you should be able to add those permissions to a security role and apply that to the specific user you are using to connect to Dynamics CRM.
Thanks!
Matt Bayes