Are flamers direct damage effect halved by the effect of a flying target?

I'd presume so as there is no specific mention of the damage being 'unmodifyable' in the card, and the source is still the flamers, a non flying unit.

If you mean the damage dealt when a Zarathur's Flamers unit sacrifices itself, the answer is that Flying has no effect on it. The RRG Flying section states that Flying only halves damage by attacks (ie applying ATK damage when resolving step 3 of an attack).

Ahh great thanks, missed that line in the RRG and I don't have it in front of me at the moment. I just read the card text on flying as saying damage, rather than combat damage.

Not even 'combat damage' but specifically 'damaged by an attack'. Means AoE isn't halved either.

Yep, it's important to remember that the keyword reminder text is just shorthand and is not considered either rule or effect, and the rules behind keywords are often more complicated than card space allows for reminder text. (No Attachments being the major exception!)