A quick check makes it look like there's around 19.5 sets of 256 8x8 tiles.
Final Fantasy 1 is a CHR RAM game, which means each individual 8x8 tile can be swapped out or even dynamically edited at runtime, rather than having to swap out an entire bank. This also means the graphics can be stored ANYWHERE in the ROM, but Final Fantasy's tiles are actually mostly in the same places.
Edit: And indeed, I suppose my NES post doesn't seem to reference that sort of tile swapping. I made it mainly for people who wanted to make mockups, and not who just wanted general info. The assumption was a mockup would be a still image and so someone making one would only need to know there are only 256 background tiles and 256 sprite tiles at once.