Amazon released their data migration service a while back, which allows you to transfer data in just about anyway you might want to, they'll migrate data between different RDS engines (MySQL to Postgres for example), and to databases outside AWS. They even support near real-time replication to database servers outside AWS, so you could hypothetically replicate your RDS instances to a fail over environment with another provider. There's very little risk of your data being locked in now.
Unless you use SQL Server. The dms service is basically useless with sqlserver. We can't get our 200gb do out of AWS. And any method that works without dms takes about 40 hours.
[1] https://aws.amazon.com/dms/?nc2=h_mo