Thanks for posting to AWS re:Post. I wanted to share my two cents on the matter here.
In this case you can use DMS - JSONB is supported as a source in PostGreSQL engines.
 Using a PostgreSQL database as an AWS DMS source - Source data types for PostgreSQL - https://docs.aws.amazon.com/dms/latest/userguide/CHAP_Source.PostgreSQL.html#CHAP_Source-PostgreSQL-DataTypes
Then, you can refer->
 Using Amazon S3 as a target for AWS Database Migration Service - https://docs.aws.amazon.com/dms/latest/userguide/CHAP_Target.S3.html
Hope this helps.
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