So how would Eye of Flame interact with World in Flames, then?

Does it get the doubling? I think it does, but I want to make sure.

I'm certain it would...as eye of flame is fire damage.

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To the before posts, even though the stacking of replacement/modifying effects doesn't use the chain is it still first in last out? So you'd say "World In Flames on the chain first, then Chromatic Cloak" The cloak would resolve upping the damage and then the WiF would resolve doubling the (now increased) damage? I'm just uncertain as I've been told when in doubt...everything uses the chain.

Since you control both effects, And they both respond to the same trigger, and are both replacement effects, you get to choose what order they resolve in.