Setting BIG-IP LTM Virtual Server for two SQL Servers nodes

I was able to view your qkview. Your node addresses appear to be public IPs. Depending on where your nodes live, maybe this should be the private addresses.

Notice that all of the BIG-IP configuration level addresses are private. There are no default routes configured on your BIG-IP, thus causing the 'no route to host' errors. You either need to use link-local pool member addresses (private) or provide a gateway to route traffic to the public addresses.

Do your pool members live in the same VPC as the BIGIP?