There are multiple ways to move VMs from one set up to another
1. You can use vcenter standalone converter and perform V2V migration, this tools was discontinued so you cannot find in vmware downloads page, However you can search in some third party websites to see if it is available to download.
2. You can add the old ESXi node to new vCenter server and do the VM migration within the vCenter.
3. You can export each VM as OVF and import the OVF in new setup.
4. If you have any storage box, create a lun and attach it to both old and new setup ESXi nodes, create a shared datastore. Move the VMs to this shared datastore and switch the VMs to new ESXi nodes then move it to desired storage.
5. You can also use the fling which you have mentioned but I would recommend to migrate a test VM and ensure it is working fine.
Some of these steps would need VM downtime.
Regards,
Suresh