You can't easily throw an OleDBException because it says cannot access friend constructor, but why not test it out with a simpler type of exception? The type of exception won't make a difference for your test.
Try
Try
Throw New ArgumentException("Throwing up!")
'Code that throws an OleDBException
Catch dbEx As ArgumentException
Console.WriteLine("Inner Specific Exception handler.")
Dim newEx As New System.Exception("Database Error Handled.", dbEx)
Throw newEx
Catch ex As Exception
Console.WriteLine("Inner Generic Exception handler.")
End Try
Catch ex As Exception
Console.WriteLine("Outer Generic Exception handler.")
End Try