Is there a way to set up a management hierarchy and use that hierarchy for permissions in an app?

The best way to create a user hierarchy in Quickbase is to have a table of users. The key field in this table should be a user field. For each level of the management hierarchy you add another user field to this table. So for example the first user field in this table would be called Sales Rep. If each sales rep has a manager then you would create another user field called Manager. If each manager has a supervisor then you would create another user field called Supervisor. If each supervisor has a vice president then you would create another user field called Vice President. You can extend this to accommodate as many levels of management as exist in you organization.

Then you populate this table with one record per sales rep. In each of these records you fill in the sales rep, manager, supervisor and vice president.

Make sure to set the noun for this table to Sales Rep. Also set the record picker for this table to display the Sales Rep field.

Now you create a relationship between this user table and all other tables where you have a user field that captures the identity of a sales rep. In each of these relationships the user table will be the parent table. When the relationship wizard asks you if you want it to create a reference field for you, or if you want to choose an existing field as the reference field, you should choose the user field that already exists in your application for capturing the identity of a sales rep.

Once you have your relationships in place you can add lookup fields to bring over the manager, supervisor and vice president user fields. Based on these management user fields you can create custom rules to grant access to only a manager's direct and indirect reports.