1896 Rainbow Toned Morgan Dollar: Natural Or Artificial?

I believe it's artificially (intentionally) toned.

There isn't one single cue, part of it comes from looking at many toned coins over time. The "flow" quality you mention is part of it. The other big key on this coin is that both sides are toned equally and with similar patterns. This is very rare on naturally rainbow toned Morgan dollars. See this site for examples. If you click on the coins, you'll see that one side might have wild rainbows, but the other side is mostly un-toned or has rim toning, or the toning has more neutral colors.

There is also the "flow" quality you talk about. The toning appears to float above the surface and devices, and is just smoothly distributed following no particular pattern. Natural toning almost always has a "crusty" quality. The link above also shows a "pull-away" feature that is very common on naturally toned Morgans, but is absent or different on intentionally toned ones. Yours shows a slight shadowing effect on the date, but it's clearly different - it lacks the consistent direction and sharp edge of a natural pull-away.

You also have to think "what was the source of this toning"? It doesn't just come from nowhere. Natural toning happens because of how the coin was stored. There are several possibilities - mint/proof set packaging, albums, holders, rolls and (particularly important for morgans) canvas bags. Each of these produces a particular toning pattern and they rarely produce the same pattern on both sides of the coin (with the exception of rim toning caused by albums or holders.)

looks too good to be true

That color screams "WRONG" at the top of its' lungs. It's a crime to see an otherwise-nice Morgan treated with that much disrespect.