Jobs and Childcare for Military Families Act of 2021 This bill allows an employer a work opportunity tax credit for hiring an individual who is certified by a designated local agency as being, as of the hiring date, the spouse or domestic partner of a member of the Armed Forces, and requires the creation of programs for uniformed services families to pay for childcare on a pretax basis. Specifically, an employer may receive a tax credit equal to 40% of a new employee's first-year wages if the employer hires a service member's spouse or domestic partner (as recognized under state law or by the Armed Forces). Currently, a similar tax credit exists for employers who hire certain disadvantaged individuals, including disadvantaged veterans. The bill requires the Department of Defense, the Department of Homeland Security (with respect to the Coast Guard), the Department of Commerce (with respect to officers of the National Oceanic and Atmospheric Administration), and the Department of Health and Human Services (with respect to the Public Health Service) to implement flexible spending arrangements that permit members of the uniformed services to use basic pay and compensation to pay for childcare services for their dependent children on a pretax basis.