Do you know what errors you are getting?
I can only imagine it is a firewall security policy issue on AWS - I assume Qlik Sense and SQL ARE NOT on the same machine, I assume Qlik Sense is on 1 machine in your on premise environment and SQL is on AWS outside your environment, which would be the case. Do you have access to AWS console to check the inbound / outbound port rules on AWS?
I think starting there would be your best bet.
You may also need to configure your SQL Server on AWS to use TCP/IP and make sure Dynamic IP is not checked either, you do this in the network connection settings for the SQL Server.
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kha - hey man (Karl) tapping into your AWS expertise for one of our fellow members. Can you validate my reply in regards to this situation? Sounds to me like firewall, inbound / outbound security port rules.
This does sound like the appropriate ports in the aws security group attached to the instance hosting sql are not open. If the location of where qliksense is running has a static external ip then i'd recommend narrowing the scope of the security groups specific ports to that IP then you will not expose your database access publicly.
Hope this helps.