The despatch notification from Magento does not contain a tracking number.
The reason for this is that Magento requires a shipment to be created and then the tracking information to be added to it. However it is at the point of creating the shipment that Magento sends the despatch notification, meaning that the tracking number will not be available.
The Magento Way
Magento requires you to click the button Send Tracking Info from your admin page. This will send another email containing the tracking information, but is a manual solution and will result in the customer receiving duplicate emails.
The Linnworks Way
Deselect the option to send a Magento despatch notification and use the Linnworks email system instead. Create a Linnworks despatch notification email and give it a condition of Source = 'Magento'
For more information on how to setup an email template: http://www.linnworks.com/support/emails/email-notifications