PoE 2 Incinerate type of damage?

I'll elaborate, since my initial answer while not entirely wrong, was not exactly right either, as I didn't fully understand how the mechanic works back then.

Ignites as though dealing 46 to 70 Fire damage means the following:

"

Deals 46 to 70 Fire Damage
Always Ignites
Doesn't deal Damage with Hits

Simply put, it's a hit that doesn't deal hit damage. Instead it ignites as if you hit with 46 to 70 fire damage. Internally it acts like a normal hit and goes through all hit calculations. In general, Incinerate will satisfy things requiring a skill that hits or a skill that ignites with hits.

Damage conversion and gain as extra damage aslo apply, but you should understand the idea. With 100% Fire -> Cold conversion, it turns to "Ignites as though dealing 46 to 70 Cold damage". Since cold damage can't ignite (by default), Incinerate wouldn't ignite at all. Unless you get something that allows your cold damage (or all damage) to ignite. And no, you won't chill or freeze instead, because it says "ignites as though dealing ... damage" not "inflicts all the ailments as though dealing ... damage"

The same is with that Acolyte of Chayula notable. Gaining % as extra chaos damage will only help your ignites if chaos damage can ignite. Intense Flames notable (35% increased Damage with Hits against Burning Enemies) should work fine as all hit damage modifiers.