Industrial Energy-Efficient Technology Act of 2021 This bill provides support for technologies to help the industrial sector manage energy and reduce greenhouse gas emissions. Specifically, the bill provides appropriations for the Department of Energy (DOE) to establish an advanced industrial facilities deployment program. In addition, the bill requires DOE, upon the request from states or Indian tribes with approved energy conservation plans under the Energy Policy and Conservation Act, to provide financial assistance to such states or Indian tribes for the development, implementation, improvement, or expansion of a flex-tech energy program to enhance manufacturing competitiveness.