Depends on what you are trying to transfer. User-created content, like photos, can be easily transferred by simply attaching a USB cable to a laptop or computer and accessing the device like any external USB storage device. Just open a window for each device and copy files over.
For data like contacts, that is attached to your Google account. I do not know what would be involved, there, because the Fire Tablet is not running an "official" Google version of Android and does not have the Google Play Services installed. After entering your Google account into the device, you should get whatever Google-based data (contacts, app data which backs up to the cloud, etc) that the Amazon's forked version of Android supports, but it is possible that much of this will not be downloaded without the presence of the Google Play Services.