Veterans, Employees, and Taxpayers Protection Act of 2019 or the VET Protection Act of 2019 This bill directs the Department of Veterans Affairs (VA) to track the use of official time by VA employees without using estimates or time ranges. Official time is time granted to an employee under federal labor-management relations provisions to perform representational or consultative functions, during which the employee would otherwise be in a duty status. The bill prohibits (1) a VA employee from using official time to carry out political or lobbying activities; (2) specified health care employees, probationary employees, or employees above a certain salary level from using official time for any purpose without a waiver; and (3) any VA employee from spending more than 25% of the time such employee would otherwise be in a duty status on official time without a waiver. The authority provided to the VA to grant a waiver shall not be subject to bargaining, and the exercise of (or failure to exercise) such authority shall not be an unfair labor practice. An exclusive bargaining agreement shall allow a VA employee to terminate a voluntary dues allotment at any time. A covered VA employee shall serve a two-year probationary period, after which the employee's supervisor shall determine within 90 days whether or not the appointment is permanent. A covered employee is any individual appointed to a permanent position within the competitive service or the Senior Executive Service and does not include specified health care practitioners.