Not really a NetScaler bod but have been given the job of updating some 13.1.53.24 appliances - do I need to run this command (nsapimgr_wr.sh -ys call=ns_aaa_flush_kerberos_tickets) after I have upgraded and rebooted the instances?

Only if KCDAccounts is being used

So if there is something in that page, they are being used?

Yup