Replicate RDS between their china and non-china accounts

DMS is one option, but they if they are planning to have homogeneous migration, native tools like MySQL/Postgresql read replica would be more appropriate.

RDS do support cross region replica. I would say go through the cross-region replication considerations mentioned in document https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_ReadRepl.html#USER_ReadRepl.XRgn.Cnsdr