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Waste-derived slurries can be burned both in a fluidized bed and when injected into a boiler furnace. This paper is the first to analyze the dynamic characteristics of ignition and combustion of a group of three slurry droplets based on coal slime, water, and waste industrial oil in a low-temperature air flow with a temperature of 500–600 °C and velocity of 0.1–1.2 m/s. The distance between the droplet centers varied from 3 to 15 mm. The results of the study can develop innovative technologies for flare and fluidized bed combustion of fuel slurries at the boiler start-up stage. It was found that a distance of 3–5 mm between droplet centers provides almost simultaneous gas-phase ignition of all droplets. A further increase in the distance critically worsened the ignition and combustion and eliminated the synergy. An increase in the air flow velocity contributed to the appearance of a common flame zone but at the same time increased the ignition delay of droplets by a factor of 1.2–1.6. The negative effects of cooling and entrainment of combustion products by a low-temperature flow can be effectively reduced by adding 5 wt% of industrial oil to the slurry. Also, the use of oil reduced the droplet ignition delay time by 15–20%. At the stages of flame and heterogeneous combustion, the differences for droplets in a group increased (the stage durations differed by 1.5–3 times). For the low-temperature start-up of a boiler, it was found advisable to provide a droplet flow with a sufficient density to stabilize their ignition without significant flow deviations (dimensionless distance 1.5–2.5).