Unless `DB_CHAINING` is set to `true` for all 3 databases, you should give the `SELECT` permissions on the underlying tables.

In case you set `DB_CHAINING` to `true`, all 3 owners of these databases are the same and **all 3 objects have the same owner** (for now it's not true in your design because your tables are owned by `dbo` and view is owned by `vdr`) permissions on the underlying tables will not be checked due to [Ownership Chaining][1]

To make ownership chaining work in your case you should do the following:

- Run:

        use Reporting; 
        go 
        alter authorization on schema::vdr to dbo;`

- set `db_chaining` to true on all 3 databases:

        use master;   	
        go      
        alter database Reporting set db_chaining on;  	
        alter database DatabaseA set db_chaining on;
        alter database DatabaseB set db_chaining on;

- check owners of all 3 databases and if it's not the same change it to the same login using

        alter authorization on database::yourDB to yourLogin

  [1]: https://technet.microsoft.com/en-us/library/ms188676(v=sql.105).aspx