Flows triggered by non-admin users fail with the error "Unable to load connection with alias ID <connection alias sys_id>"
If the flow is configured to run as the user who initiates the session and the user is not an admin, he/she would not have access to the actual table where the connection is stored - http_connection. This causes the flow to fail with this error.
Since the flow requires access to the connections and credentials, it needs to run as the System user.
In the Flow properties, set the Run as as the System user.