Usually, fires are allowed in dispersed camping areas on BLM land unless otherwise stated by the managing agency. I couldn't find anything specific on the BLM site, but these tips are from utahfireinfo.gov:
Clear campfire site down to bare soil.
Circle pit with rocks.
Build campfires away from overhanging branches, steep slopes, dry grass, and leaves.
Keep a bucket of water and a shovel nearby.
Never leave a campfire unattended.
When putting out a campfire, drown the fire, stir it, and drown it again.
Always have adult supervision.
Be careful with gas lanterns, barbeque grills, gas stoves, and anything that can be a source of ignition for a wildfire.
