Is there a simple way I can have a powershell / cmd prompt open and stream the dns cache so that it will scroll automatically as things are being cached?
Take a look at the MicrosoftDNS_Cache WMI Class in the root\MicrosoftDNS namespace. My desktop doesn't have that namespace available, but supposedly it's available for servers.
That might give you a start in the direction you're looking for.
If that has the data you're looking for, you could wrap that into an endless loop like so:
Obviously you'll have to tweak the get-wmiobject code to get the output to look how you want, and as mentioned above, that's assuming the class/namespace contain the date you're looking for.