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what the title says.
Lord of fire says that it affects any weapon described as using 'flame' or 'fire' as its effect of special rules. Flamers have 2 different weapons, warpfire and breath of chaos. Breath is a template weapon and warpfire is assault 3, and neither has any mention of flamer or fire in the special rules/effects, so i would have to say no, lord of fire does not affect flamers of tzeentch.
I am not positive, it depends on the exact wording in the Daemon book, which I don't have near (or in this state right now...)
Lord of fire reads "All flamer weapons (as well as heat rays, burnas, skorchas, interno cannons and any weapon described as using 'flame' or 'fire' as its effect or in its special rules) and weapons with the melta type fired within..."
SO, I would say that most likely, yes, they would be effected by this. I would be surprised if their weapons were not, in any way shape or form, described as being flame weapons. The codex doesn't say that they need to be fire or flame in special rules exclusively, simply that it must be described as such.
Warpfire especially seems to make sense, fire is in its name, and likely described as balls of flame or something along those lines. You would probably need to see how the Daemon book describes breath of chaos, as name and template mean nothing. If it doesn't mention fire at all, we COULD construe them as simply having very rank and horrid morning breath. Hah