Part of the reason you're seeing a black object in the background is due to one of the lights being in front of one another. You could move it out of the way to avoid the shadow, change it's type, turn it off from within the GUI and loose it's lighting data, or remove it from the exported lights. I think this might have been touched on somewhere in the thread.

Another possibility to consider, aside from turning the flame itself into a mesh light, your best bet would be to set it to emit light from by modifying it's material and exported geometry, detailed a bit on the LuxRender wiki.

What's interesting is that having an object emit light instead of being a full blown mesh light is that the scene appears to render much more quickly than the norm and the scene still receives light from the said object. Sadly, since that sort of functionality has not been implemented in LuxPose, you'll have to hand edit each flame object emitter mesh and and it's assigned material. Possible example as follows:

<em>Add this after the NamedMaterial section for your light
emmitter:<br></br>
    LightGroup "flame"<br></br><br></br>
    AreaLightSource "area" 
"texture L" ["Flame:light:L"]<br></br>
   "float power" [2.000000]<br></br>
   "float efficacy" [20.000000]<br></br>
   "float gain" [1.000000]</em>

You'll need to play with those settings to see what works for your scene, then add something similar to the following after your generated material for that object:

<em>Texture "Flame:light:L" "color"
"blackbody"<br></br>
   "float temperature"
[6500.000000]</em>

If you want to be able to able to control each individual flame, you'll obviously need to change each one's LightGroup name. Also, you don't need to add anything else to your exported lights file (.lxl) as it's not a real light, per say. Again, I also highly recommend that the object is textured and, possibly, transparent for a more interesting effect.