The EPA advises against any kind of trash burning and some localities prohibit it. While the trash may seem innocuous, harmful dioxins and other chemicals don't release into the air until burned. From the air, these chemicals transfer to soil and waterways.
Even just burning paper can be toxic, as most inks contain heavy metals, which end up in the soil after being burned. Heavy metals contaminate groundwater and the soil. Plants aren't affected by the heavy metals, but people who ingest metal-laden vegetables can develop cancer and lung problems, among other diseases and disorders, the EPA reports.
The best garden to plant where trash has been burned is one that you can look at, but won't be eating. Flower or landscape gardens may help dissipate the heavy chemicals and metals over time, but before planting a vegetable garden in these areas, have the soil tested.