The Witch's Banquet Place Setting (in the W-Shop for Halloween) has candles that flicker subtly but continuously.
The candles in the lamps from the medieval rares flicker the same way.
As you know, the Ancient Brazier has a huge flame that can be turned on or off. The Centurion Candelabra has a somewhat smaller flame that can also be turned on or off. Someone else will have to tell you (and me) whether the flame on the Aztec Fire Pit can be turned on and off since I didn't have enough money last time it was offered for sale. (By the way, the Ancient Brazier will not go in an underwater room: my son tried.

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Can the Tiki Torch be turned on and off and how big is the flame?
I really couldn't tell you about what the e-store carries since the only thing I ever buy from there is the charms.
The Ancient Brazier goes very nicely with the Halloween theme almost as if it were part of it, and most of the other fiery objects that I have (the Centurion Candelabra, and the two lamps from the Medieval collection seem to go decently enough. The Ichiban theme has those humongous paper floor lanterns that can be turned on or off. There is no open flame showing, just a glow, and I am not too sure how I feel about how those look in with the Halloween paper and floor. (Sorry about the digression; my current decorating project is the Halloween room. There's nothing like waiting until the last moment, and it looks like it's going to mean that I won't get as many of the refrigerators as I wanted. Luckily, I have the bare minimum that I need.)
I think there are a number of items like the Paper Lantern which light up when asked to but which do not have open flame or fire. The Antique Lamppost (adoption exclusive) is also one of these.