How did Billie Jo's mother die in Out of the Dust

She burned up because Billie threw a bucket of kerosene at her

What happened was that Billie's father left a bucket of kerosene in the kitchen, which Billie's mother thought was water. She put it over the stove, and it caught on fire. Pol (the mother) ran out of the house. Billie, afraid that the house would catch on fire, took the bucket and threw the kerosene out the door ... which ended up splashing on her mom's apron.

There, Billie's mother burned up. Though she didn't die there, it was what caused her to get very weak, and when she was having the baby, Franklin, she died.