After multiple attempts we did get a response - albeit vague - from AWS.
At the foundation of Amazon Chime security is Amazon Web Services
(AWS) Security. AWS regions and networks are built and operated to
meet the requirements of some of the world’s most security-sensitive
organizations. AWS constantly undergoes third-party audits by a
variety of public sector and private sector auditing organizations in
order to maintain its status under multiple compliance offerings, such
as the credit card industry’s PCI DSS Level 1, the U.S. Government’s
FedRAMP program, C5 Certification in Germany, and IRAP assessment by
the Australia Government. For more information, see the AWS Security
and AWS Compliance websites. Amazon Chime is designed and operated
according to the same AWS standards, has undergone the compliance
process required to be a HIPAA-eligible service, and is currently in
the process of being added to other relevant compliance programs.
The Amazon Chime SDK can be used by customers who incorporate GDPR
best practices and compliance using our Shared Responsibility Model.
So they seem to imply it can be used in a GDPR compliant way.
Additional info: Specific to chat feature, AWS advised us to use the data-messaging API route to ensure the data relay and retention within EU.
All chat messages in the Chime app are relayed and stored in us-east-1
(Virginia). The chat messages always leave the UK.
There is a data messaging API in the SDK that can be use to build
chat.
(https://aws.github.io/amazon-chime-sdk-js/modules/apioverview.html#9-send-and-receive-data-messages-optional)
These messages flow through the same region that is used to host the
meeting (London, for example) and they are persisted there for a few
minutes and until the end of the meeting so that they can be relayed
to other participants during that meeting.