Chapter 14 of "Access 97 Developer's Handbook, 3rd Edition" by Litwin, Getz and Gilbert is primarily devoted to programatically checking against and changing Access security.
More importantly, there is code included that contains functions related to your request. You could use this code, then simply go through the tables collection and check each individual right for each table in a nested loop. I stop short of adding the code to this post as it would be a copyright infringement
Specifically, you can read permissions of an object (table or otherwise) by checking the value of the Permissions or AllPermissions property of the object. (Assuming you have Administrator rights yourself.) Permissions will check individual permissions while AllPermissions will return the union of all permissions in one value. Both return a long integer.
ex: lngPermission = db.Containers!tables.Documents!tblorder.Permissions
Using AllPermissions, you could parse the returned long integer bit by bit via bit masking to determine all the rights for that object.
ex: canread = ((doc.Permissions And dbSecRetrieveData) = dbSecRetrieveData) returns true if read rights are available, false if not. (Doc is a document set to db.Containers!tables.Documents!tblCustomer)
There is quite a bit about it in the book and I will try to find time to read up on it.
in object browser you can find the security constants under DAD.PermissionEnum This will show you what is available.
I have never used bit masking and most of the above is copied from an old posting elsewhere

S I have some heavy reading ahead
Peter