Each and every Sync installation gets a unique digital certificate generated basing on the selected identity name. Even if you give same name to two independent Sync instances, their certificates (identities) will still be different. The certificate helps to identify the peer when it connects to a share, and its fingerprint can be viewed in "My devices -> Identity details" menu.
If several devices are linked with one identity (through linking devices option), they share common certificate (have same fingerprint). If you attempt to link two devices bearing different certificates, one of these devices will take over the certificate of the other device. When that happens, Advanced folders and license on the device which acquired a new certificate will be removed from Sync UI. You will get a notice that your Advanced folders are about to be removed from the app:
Note that Sync behavior towards Advanced folders depends on the platform.
On Android, Kindle Sync will only remove the folders from the interface. Neither folders nor any user data therein will be deleted from your file system. If you wish to continue syncing these folders, simply add them back to Sync once the new linking procedure is complete.
Due to iOS and Windows Phone architecture peculiarities, Sync will remove all Advanced folders from Sync AND delete them from the file system.
Standard folders will be unaffected on all platforms. This is due to their architecture which presupposes the use of distributable keys, not digital certificates.