Your best bet would be to purchase a 4TB external and move over 4TB worth. Build your flexraid server and use two of your 2TB drives now to start. Move the data over, then do it again, and once again. Then just add the 4TB to your flexraid pool (probably as your parity drive)
That way you can avoid the cost of buying drives, and only need the cost of the mobo, cpu etc.. (which you are going to do anyways it seems)
Or- you could buy all new drives- and then sell your old ones. It's tough building a server from scratch because HDD's are costly once you get serious about storage.
15TB means you need at least (3) 4TB drives and at least (5) 3TB drives do have enough room to copy everything over on a flexraid server. That is costly ($35 per TB) in just drives. The major reason I like flexraid is because it's so flexible and you can add drives with data on them- and drives are readable which makes server upgrades a breeze. Unraid, it's trickier to rebuild without data loss. You can reuse your drives in your new server- but you would have to buy at least 1 drive and then copy over each drive's stuff and then add it to your new server 1 drive at a time.
That might work well if you can wait for each drive to copy over....