Kerberos and SWG Implementation

I would suggest looking into DNS resolution and/or routing to see if you can reach the DNS controllers. This has nothing to do with SWG here - but rather an issue that prevents F5 device to properly discover/connect to the KDCs.

Is this for transparent or explicit proxy deployment? If explicit, you will need to add the variable assignment before Kerberos Auth agent:

You need a Variable Assign agent on the Negotiate branch before the Kerberos Auth agent. The value of the Variable assign is:

session.server.network.name =

Also, just curious, why did you choose Kerberos over NTLM for your deployment/use case?