Regular NAS servers use mechanical HDDs, but if you want to make the switch to flash storage, there are a few decent choices available. The benefit of using an all-flash NAS is that you get significantly higher bandwidth; most traditional HDDs can hit 250MB/s at a maximum, but with an SSD, you easily get ten times that bandwidth.
I tested all the SSD NAS servers available today, and TerraMaster's F8 SSD Plus is the best of the lot. It holds eight SSDs, comes with thermal pads that ensure the drives don't overheat, and you get active cooling.