This issue is caused due to AWS RDS permissions.

While restoring, when we select restore from a file, Microsoft SSMS searches at the physical location where the database is running. But AWS RDS is designed in such a way that we don't get file-level access to the RDS instance. Instead, we get an endpoint and port to connect it.

See [Importing and Exporting SQL Server Databases][1] in the Amazon Relational Database Service (RDS) User Guide for more details.

  [1]: http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/SQLServer.Procedural.Importing.html