I'd think the easiest way to do this would be to:
- Set up the Linux DNS server as a slave / secondary server to the Windows box.
- Do a DNS zone transfer from Windows to Linux
- Optionally, shutdown the Windows DNS server, after you have testesd / become familiar with Linux.
There is an O'reilly / Syngress book Windows to Linux Migration Toolkit that covers this.
It's funny, but I could only find links on the web that do the opposite. It must be an MCSE requirement or something. I added some of the links I found just in case they may provide you with some insights.