There is no petroleum product that would not contaminate your soil. The best way to get those roots out of there is to dig them out, a process that will also give you a chance to take a good look at the soil and see what might need to be done to make it into a better soil.

I must agree with kimmsr that there is no flamable petrochemical product that won't wreck your soil for years. For a controlled burn, try methanol (wood alcohol) - it either burns or evaporates completely from the soil. Any microbial or micorhizae damage is temprorary. STAND BACK or use a long stick with a wick when you light it! It burns very hot. Digging is good, but be sure to get every root.
Hortster

Since burning yard waste produces more air pollutants than does a coal fired power plant there is no good reason to burn any kind of yard waste, ever.