Yes, definitely too red!
The first thing I might look at is the Tint color although... it can be good to have some solid red in a fire represented.
The next would be the opacity. I think with as many particles being emitted you might be able to get away with an opacity setting below 5%.
That might not seem like much but when Additive Color is turned on and each particle color shows through to the one behind it 5% might even be too high.
After adjusting Opacity to 10% and changing a few other settings such as Tint I started to see something reasonable.
The speed of the flames is definitely running too quickly.
Here's a single frame of a much much milder frame that doesn't quite hit the target I was after.
I went too far in the other direction.
Is that area around the camp all scorched earth?
If so... nice touch!