Dave,
You are in luck, i just did this myself.
From the VMA you can populate a file like hosts.txt with all the hostnames and run it against that. Save this in a file like syslogreload.sh and set chmod u+x or copy and paste the text below /bin/bash once you have hosts.txt populated
#! /bin/bash
for host in $(cat hosts.txt)
do
echo starting $host
esxcli -s $host -u root --password 'pass' system syslog reload
echo $host done
done
In powercli you can do the same like this if connected to Vcenter already and you are comfortable. You can also change to Get-Datacenter and pipe that.
$cluster = Read-Host "Enter Cluster Name"
foreach ($server in (Get-Cluster $cluster | Get-VMHost | where {$_.ConnectionState -eq "Maintenance"})){$esxcli = Get-EsxCli -VMHost $server
$esxcli = Get-EsxCli
$esxcli.system.syslog.reload()
}