Burn Pits Accountability Act This bill requires the Department of Defense (DOD) and the military departments to evaluate whether each member of the Armed Forces has been (1) based or stationed where an open air burn pit was used to dispose of waste, or (2) exposed to toxic airborne chemicals. Members located where an open burn pit was used or exposed to toxic airborne chemicals must be enrolled in the Airborne Hazards and Open Burn Pit Registry, unless the member elects not to enroll. The evaluations must be included in periodic health assessments, physical exams conducted immediately prior to separation from active duty, and deployment assessments. DOD must share the results of the evaluations with the Department of Veterans Affairs.