This is the best way:
1. Export your desired mailbox folders from your Zimbra Client (whether web or desktop) to .tgz archive.
2. Setup a new account in Zimbra and choose Gmail predefined settings (it uses IMAP by default but you have to make sure that your Gmail account has IMAP enabled first).
3. Import your .tgz archive into your newly created gmail account in zimbra and allow it to sync!
That's it
Note: To avoid waiting for the whole archive to get synced with your gmail account, you can choose to export the sent items only (or maybe other folders) while the rest you can fetch using POP3 directly from the gmail.