I'm not sure there is a good way to get a "crisp" HDR photo of a bonfire. Using multiple bracketed exposures at different exposure values will make the flames from one exposure look brighter or dimmer than the flames from the other exposures.
To get crisp images of flames, you need a fairly fast shutter speed. The gases venting off the fuel are changing rapidly! This is a wood fire at 1/1250 esc.
EOS 5D Mark II, EF 24-105mm f/4L IS, ISO 1600, f/5.6, 1/1250 sec.
Color Temp. 2500K, +1.33 Exposure and other minor adjustments in post.
This is what the same fire looks like at 1/60 sec. With the exposure adjusted for the crowd.
EOS 5D Mark II, EF 24-105mm f/4L IS, ISO 6400, f/4, 1/60 sec.
Color Temp. 2800K, -1.50 Exposure and other adjustments in post.
I was shooting manual and may could have captured more detail of the flames if my exposure had been less, but other shots that night with less exposure but an equally slow shutter were a motion blur of flames.
I was standing in roughly the same spot for both photos. The first was at 73mm, the second at 24mm focal length. The second was also cropped a little more than the first in terms of height.
There are about 4 1/2 stops difference in these two images by the time you account for post processing. The flames on the first have a few isolated areas that were at 255,255,255 before exposure compensation was applied, but most of the bright spots are in the high 240s and low 250s. By increasing exposure 1.5 stops I blew many areas of the flames out in order to recover detail from the pallets and ground, but there is still a lot of detail left in the fire. The flames in their entirety in the second were at 254, 254, 254 when exposure was reduced -0.67 in post, so they were clipped by about 2/3 stop.
To get any detail in the flames for the tone mapping to work with, the rest of your scene is going to be very dark. Even though the fire is quite bright, the heat is so intense that the people are kept a safe distance away and the inverse square rule comes into play.
Using fairly heavy handed tone mapping on the first image does recover detail (and considerable fixed pattern noise) from the deep shadows but has very little effect on the flames!
I felt my best efforts of the night involved images that captured the reflected light of the fire.