I know this thread is getting a bit old but I was searching for the same solution and managed to make multiple DNS servers work in Packet Tracer as requested.
You need to add some records to the DNS servers that point them to the next server (up the tears). Those being an “NS” record that then points to the “A Record” for the next server. I created an NS record type buy the name of “com” that pointed to “root”. “root” is an “A Record” that then points to the next DNS server IP address.
I would like to attach a packet tracer sample for you to see, but I am unable to attach the file to this message. As such, pics will have to do.
The servers on the internet switch are all separate networks separated by different VLANS, so for each server communication it always has to go back though the router Router1 thus simulating many routers quickly and easily for this simple purpose.
I am by no means an expert but this solution seems to work. If you open a web browser on PC0 and head to www.pt.com the page should open. Not only that, when you then check the DNS servers, you will also notice that their cache also have the details.
There is also an example on packet tracer itself (in the PacketTracer\saves\server\DNS folder named: Multilevel_DNS.pkt) that goes into the setting in a bit more depth. If anyone else has any suggestions, buy all means let me know.
Lastly, I did find a video…. Got about 5 mins in but for those who are willing to persevere… it may be worth a look. https://www.youtube.com/watch?v=JmWu2jYQSXw
Hope this is of help to someone.