Working Families Flexibility Act of 2021 This bill revises requirements for the receipt of compensatory time off for private sector employees. Specifically, the bill authorizes private employers to provide compensatory time off to their employees at a rate of one and one-half hours for each hour of employment for which overtime compensation otherwise is required; employees may accrue a maximum of 160 hours of compensatory time. Employers are prohibited from interfering with an employee's right to or not request compensatory time off in lieu of payment of overtime compensation or from requiring an employee to use such compensatory time, and must give their employees 30-days notice before discontinuing a compensatory time policy. Employers are liable to employees for damages from violations of these requirements.