Hello, there is not a (obvious at least) way to export an RDS snapshopt on premise. The RDS snapshots are stored in S3 but those S3 buckets are managed by AWS not the customer.
If you want to store a database snapshot on-premise you need to use the native back up tools that the DB engine supports For example you can use mysqldumb for MySQL databases.
Another question to ask your customer is why do they want to export the RDS snapshot on premise? Your customer could consider copying the RDS snapshot to a completely different account (that would serve as the back up account) with very tight permissions or even to a different region all together if they want to have "offsite" backups of their data. http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_CopySnapshot.html
A limitation that might apply is that: You can't copy a snapshot to or from the following regions: AWS GovCloud (US), China (Beijing)
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