On zoneedit, set up the domain on the slave server. You will need to set up primary/slave relationships between your server, ns1.server1.com, and theirs. This is so your zone file can propagate to their servers so that they can answer queries. I'll leave this as an exercise for you.
I am not familiar with this is this exercise involve reinstalling linux using the multiple server replication setup or it is simply to put the ip address of zoneedit two servers in the allow zone transfer box. Everything works okay except for synchronization. Any suggestion to sync this properly?