Q.Wood Ash
Is burning brush in a garden good for vegetables?

Certified GKH Gardening Expert
While you may not want to burn directly in the garden, it shouldn't pose a great threat, as in most cases this will provoke additional growth--albeit in the garden you'll only want vegetables growing and not weeds. The best option would be to burn brush elsewhere and then add the ashes to compost, which can later be added to the vegetable garden. This article will help you: https://www.gardeningknowhow.com/composting/ingredients/wood-ashes-compost.htm