Wind Workforce Modernization and Training Act of 2019 This bill provides incentives for programs that prepare students for careers in the wind energy industry. The Department of Energy (DOE) must establish a program to award grants to community colleges or technical schools that offer wind training programs. Such colleges and schools must use the grants for large pieces of wind component equipment (e.g., towers or blades) for use in training wind technician students. DOE must also establish a program to prepare veterans for careers in the wind energy industry that shall be modeled off of the Solar Ready Vets pilot program. In addition, DOE must convene a task force to study the wind technician workforce.