Well let's take a look at some fires! We'll search for "camp fire embers"
So let's dry and dismantle this into the basic colours.
Our deepest colour here is white, which isn't that surprising. These are in the absolute hottest parts of the fire, so this is going to be like the skull and the torso, probably not extending out much into the extremities. Easy way to do this is to base-coat the entire model with white paint, no?
Next there's some very light yellows. Looks a bit like ushabiti bone or khaki to me. I'd go with the first. Paint this over the top of everything, missing only the deepest of crevaces.
After this we've got proper YELLOW, not the light khaki like before. Maybe a tiny little bit of orange or brown thrown in with that. Like before, except straying a little further from the crevaces and leaving our previous colours behind.
Then you need to fade out towards more orange colours. Each step is pretty much just going to be painting over the top of the previous colour but not painting over it completely. The key here is THIN layers.
Now after this at first glance we're just jumping straight to black - but wait! I'm seeing another colour between this orange and the black. It's basically a very dark brown; the bits of the ash that's ever so slightly illuminated by the surrounding orange.
Fire/Embers comes in three main colours:
White is the hottest
Orange is the coolest
Yellow is everything in between.
As someone who has lit plenty of fires in her time (Camping, not arson), I've never seen a red fire outside of a chemistry lesson.
So far we've pretty much gone White > Light Yellow > Yellow/Orange > Orange
Then after that we're moving onto the bits of wood (or bone, on the model itself) which aren't actually on fire. So from here I think we want to now go over the edges of the model (Leaving some of that orange in there) with our dark brown colour. I don't use GW paints so I don't know any of their new browns. This dark-brown is just going to be the bits pointing towards any glowing areas; keep this in mind when painting!
Other than this, we just want some black bits really.
Rather than trying to paint white>yellow>orange coming out of every crevace, I think that you should go for white on the hottest crevaces and orange on the coolest crevaces. I'll throw something together in photoshop to illustrate what I mean:
It's not fantastic, but hopefully it gets my point across. I've included a version on the top which does not have the brown edging to the black.
Basically, because the bones act as silhouettes, the white hot behind it isn't going to transition up through yellow and orange before the silhouette. You're going to have a very stark contrast of white to dark brown and then black.
And more fun than helpful, but you can see that it's white-hot in the middle and then gets to the cooler orange colour at the extremities:
For large flat areas on the miniature which just look like a kind-of boring black, why not add some cracks and stuff as if the fire is burning through and causing the bones to crack from within?
One of the annoying things is that when you shine a light on a fire like I put at the start of my post, you see the light grey/white ash of everything. It's only in the darkness where the wood (or in this case bone) is in front of the flames and becomes a silhouette that you get the black look. Maybe you could add some ash colours to break it up a bit? I'm sure that you'll find somewhere that sells an ash pigment.