Overview on modifying the Synology Server, bootstrap, ipkg etc - SynologyWiki will help you set up development platform for Synology
After you have running compiler environment, you need
Building the software yourself - Zimbra :: Wiki
Now, spend two weeks building, fixing things, rebuilding etc, and you might end up with system that barely runs.
If you actually feel brave enough to do this, write all your steps down so you can do it again when neccessary.
As this self built system isn't supported, you have to rinse and repeat the process every ~3 months or so when new version of zimbra is out.
Or, you could use real computer and one of the supported distributions, and have running system after 4 hours of tinkering(even faster with the vmware appliance).
It all depends on how much of your own time you are willing to spend.¨
I'd personally take the supported platform route.