Is there a way to do data export from Amazon Web Services RDS for SQL Server to On-Premises SQL Server?
Best is to load the data into a staging database on premise and then incrementally load the data to the main database.

You can use : SQL Database Migration Wizard found on codeplex.

Even though it is for Azure to onpremise sql server and vice versa, it will work for Amazon RDS as well.

Other alternative is to use SSIS as mentioned by @sqlreader.